Not from a medical perspective but personal experience (the doctors hate me for a reason).
I was riding in the snow because we don't have an indoor ring where I board and my horse spooked, tossing me onto the very much frozen ground. The way I landed caused a few of my ribs to go snap crackle pop and my insides decided to join my outside (it's honestly not the first time, wish I could say otherwise). Now because this city is unequipped to deal with the cold, snow, or ice the ambulance took a while to get there and I don't deal well with cold at all. (thankfully we have an on duty trauma trained pair of medical people on staff because when you get into a disagreement with 1500lbs of muscle it doesn't generally work out in the 100lb humans favour).
Now it is different from your scenario in that I most certainly wasn't left alone and I had trained medical help not to mention location.
The first thing (aside from pain) that I noticed was that because I had been exercising, I had been sweating inside my layers. When I stopped those layers kept in the moisture and things started getting cold real fast. (In my case it meant cutting off the previous layers as best as possible with least movement and adding fresh layers.) the problem if there's something, like fabric, between you and the ground, is that your body heat will begin to melt the (ice in your case) frozeness of the ground beneath you but the cold temperatures will try to refeeeze that and the resulting water will soak into the fabric you're laying on whether that's a blanket or clothes. Then it gets real fun. Everyone's taught to apply pressure and elevate. For the most part it's instinctual to grab for the part where your insides are trying to make a break for it.
Being a rider we're taught from day one to stay still and not grab anything but there's a sort of mental shock (not to be confused with actual shock, as in the medical condition) where you are in a state of suspended disbelief about your situation and you try to do some really stupid things (like get up or in my case prop myself up and look for my horse). Then your mind goes 'hey hello what are you doing? You do remember your in pain right? Here, have a heaping dose to remind you!' (My mind sucks sometimes)
Then you're body decides to start shivering. This is the bodies way of trying to keep you warm, you also start to lose feeling in the peripherals. Hands, feet, arms, legs. As you get farther into hypothermia those go numb. You also begin to cool quite a bit at the site of bleeding if it's a significant amount because again, blood is a liquid. If it's pooling beneath you I imagine it would be like laying in a puddle. If it's being held close to your body because of several layers of absorbent pad then it's like having a half frozen snowball held to your wound. If you aren't kept warm shock will set in as your body loses its heat. Don't forget that if you're in liquid your body cools much faster then outside of it. In the case of apply pressure the coldness that comes with blood soaked bandages in cold weather helps constrict the vessels around the site and the cold definitely appeared to radiate out from the pads.
The mind slows down, starts to drift from the more rational thoughts of survival, family, and the like, to more trivial things like how expensive that down jacket was and who's going to pay board fees now (here's a hint if you're dead, the answer is nobody).
The more cold you get the bigger the tremors of your body and the more tissue damage you're doing. (In my case the bleeding had actual sped up after it started numbing my arms/legs probably because my body was directing more blood to my internal organs which were mostly located in the chest area and the ribs are again in the chest area. The blood vessels around the necessary organs expanded while the unimportant ones (personally I find my arms and legs rather important myself but my body has other thoughts) constrict, limiting blood flow. In my case as the ribs and thus surrounding tissue (inside and out) were located near the important bits (lungs and heart for instance) it sped up blood flow. Which in turn decreased my core temp faster as blood wasn't all making it to where it wanted to go. If I had say, a broken arm, between the cold and my blood redirecting to internal organs my blood loss would have decreased as the trauma site's vessels constricted to preserve warmth. The body priories itself. Yes, blood loss is bad. But if your internal organs are shutting down from cold all the blood in your body won't help you.
The colder you get the harder it becomes to think until you reach a point of cold where it doesn't *seem* to matter anymore how cold you really are. If you aren't in shock by then you sure are now. You're conscious brain stops processing the danger beyond registering that it's there (Mine was more 'It's serious.' 'I *should* care more' but in an abstract way. Like standing in the cashier line and briefly noticing that the kid in the stroller over there is cute before the mind snaps to something more immediate... Except there's no snap back and your caught in the dispassionate observation with mild emotional output mode)
You start to focus on really weird stuff when your body starts shutting down. Your blood starts slowing as everything begins to shut down into true survival mode.
If you've ever had your wisdom teeth taken out and they put you under anesthesia, when you come out of it you're initially tripping pretty hard but at some point you gain enough clarity to realize how badly you're slurring and an awareness of how your body isn't moving quite coordinately but you can't seem to stop. Or when you've had one too many drinks and you realize you're drunk and should probably stop listening to that voice in your head that says 'of course you can dance' but you can't quite make yourself do so and continue to demonstrate your 'epic' dance skills much to the amusement of your soon to be YouTube audience. I for one was absolutely enthralled by the contrasting colours and the sound of rather panicky paramedics (when the paramedics are worried you have a problem.)
The whole fade out thing? Never happened to me. Was sleepier then when I pulled a 72hr cram session but if anything i saw things that I did focus on in a sharper way, just in a very very narrow way. And attention easily distracted. Had trouble forming words and couldn't answer questions asked. I couldn't focus on their words long enough to hear the question and I'm pretty sure my brain was too shot to processes even what I did hear.
But hey, the paramedics arrived so I didn't get the full knocking on Death's door and being invited in for tea experience.
Another thing I've noticed (as the stable I ride at has a policy (mandatory at least three days paid for, though they'll pay the entire thing for up to 5yrs) of seeing a psychologist in the event that they have to call the paramedics for a life threatening injury) is that other senses heightened, except sight which only seemed to heighten in a very narrow perspective. Maybe because it was a life threatening injury and my body went into fight mode, but since you can't really fight yourself so...
Senses like hearing, mostly things close by while those further off were ignored or unheard. Sounds like the rustling of fabrics (such as my instructor's waterproof jacket against the giant first aid kit of doom. The sound of the zipper on the kit and the plastic being pulled off the various pads and bandages were louder then say my fellow students talking. I couldn't tell you what kind of noises the horses made 'verbally' (for lack of a better word. Ie snorts, neighs, etc) but I could roughly judge where everyone including the horses were by the sound of footfalls. Tactile sensation (not to be confused with pain sensation who seemed to be throwing a very enthusiastic party along my nerves) like the coarseness of different fabrics and pads, the way they moved against each other and myself. The way the sand/snow shifted with movement and the tremors in the ground when heavily bundled and booted people moved around. (Perhaps since your character is on ice you could use the uneven texture, the bumps and groves and the like?). Taste was another odd one. It's hard to describe because unless you're eating food it's not a sense one normally uses. The closest I can come is a cold taste like ice cream but without any of the flavouring in ice cream? Like eating ice chips when you have a bad fever maybe but less solid on the tongue? And more dry rather then the creaminess of ice cream or the wetness of ice. Smell was another unpleasant one. Very pungent. Smells like blood (obviously) the smell of people even if they are clean people have their own smell to them, typical smells of the barn for me. Despite being winter that woodland smell (yes my stable borders some woods which make for great trail riding when weather permits).
Hope it helps,
Again, doctors tend to hate me. I love my high risk sports and adventures. That and my tendency to self-treat by either bandaging or stitching myself together does not endear myself to them. (Yes I have the training and know what I'm doing. Plus with all the various injuries over the years I don't quite have complete pain sensation anymore. I have been known to walk around on a recently dislocated hip because I have stuff to do and strangely enough those spandex pants worn under clothes and cut off above the knee work just as well as if you bandaged up a previously dislocated shoulder to encourage it to not go travelling anywhere it shouldn't with or without the roadmap. I've also walked into ER with my arm bone (whichever that one is) trying to jump out. Bent and twisted my body in all kinds of directions it shouldn't go (hint: if your toes are facing the wrong way, you're ankle may be broken twisted dislocated or some combination of all three. You should also not use the 'this little piggy went to' children's rhythm while the doctor pokes your toes to see if you can feel it... It creeps them out, specially if you giggle and they haven't put you on painkillers yet.)