As long as you are happy to talk, I am happy to listen.
In this situation, I would assess the newcomer's riding experience and the types of horses. If he/she did not know how to ride a horse, this might eliminate mount possibilities for him/her. A nervous horse, or an animal with unfortunate habits (my mom and I once had a horse that would try to scrape inexperienced riders onto the walls of the arena if frustrated, and we had one that would bite at the toes of any rider not savvy enough to realize what was gong on), would require an experienced rider. Similarly, a sensitive, valuable horse's mouth could be "ruined" by an inexperienced rider who cannot keep a light hand, or who can't keep his/her hands away from the horse's mane or the saddle; a valuable horse can learn bad habits from an inexperienced rider. Actually, come to think of it, I wouldn't trust anybody I don't know well: the newcomer can't ride my "special" horses. He/she just can't. And if I saw him/her mistreating a horse, or sawing at a horse's mouth due to inexperience, I would make him/her get off and walk. Horse people are funny that way.
You need to decide what kind of tack is being used. A PP mentioned a "saddlehorn", but those are only found on Western saddles. You could have Western saddles in the American West, or another part of America, but probably not in Europe (I'm American and have been living in Europe for a decade, and have yet to see a Western saddle here, which is fine by me). A Western rider holds the reins in one hand, and (ideally) guides the horse with reign-on-neck signals and heels, though--because of the saddle horn and big saddle--many inexperienced riders are given Western-trained horses and tack so the can hang onto the saddle horn and pretend they know how to ride a horse. This usually results in sawing on the horse's mouth (resulting in a "hard" mouthed horse).
English tack features a smaller saddle that is placed nearer to the horse's withers (shoulders). There is no saddle horn. A rider in an English saddle doesn't "hang on" to anything; balance and legs keep you on the horse. You guide a horse with heel pressure (no kicking) and slight pressure on reigns (an experienced rider's "cues" to the horse should be invisible to onlookers). If your book is set in Europe, this is probably the type of tack. If this is historical, consider whether there might be sidesaddles for women (this will depend on time period and the women's social class, I suppose).
When horses travel in a group, they like to stick together (herd animals). If one horse spooks and runs, others in the group may try to follow. You don't want to put a "spooky" horse in the front of a trail ride. Some horses are kickers, and--I'm not making this up--the custom is to tie a red ribbon in the tail of a horse that is known to kick other horses and people. Of course you don't want to put a kicker in front of other horses in a trail ride, either. Some horses are "buddies", and will try to walk close to each other; it is quite sweet to see this.
A slender horse with long neck and back won't be able to carry as much weight. This type of horse is what you see in flat racing (like the Kentucky Derby), steeplechasing, and dressage. Historically, these would have been "light" mounts used for hunting or riding, fast and agile, but not great for long distances. I would not put a lot of weight in saddle bag supplies on a horse like this.
Any draft breed (Clydesdales, Percherons, Shires, etc.), or non-breed with draft confirmation, would be good for pack weight. These are the work horses you see pulling the Budweiser wagon. They are large, thick horses with feathered legs. They aren't fast and aren't used for sport, but they are strong and have placid temperaments. If any of these are in the group, I would expect to put more weight on them, and even though they are big, I would expect them to be calm enough for an inexperienced rider.
A smaller horse with a short back and high-set neck (Arabians have this confirmation) is going to be the best for distance riding. Even so, I would not pack too much weight on this type because this is the horse that would happily carry a rider and remain "fresh" longest. I would put this type in the front of the group to keep everyone moving along.
If your group is made up of medieval peasants, for example, they aren't going to have blood horses/actual breeds of horse in their group. The "mutt" (grade) horses can be divided into tasks based on their confirmation and temperament, though.
It is a very, very bad idea to let hot, sweaty horses drink large quantities of water. Doing so can result in colic, which can kill a horse. So when your group encounters a stream, riders should allow horses a quick drink, but the horses should not be drinking huge amounts. At the end of the day/ride, any horse that is very sweaty/hot will need to be walked by hand until the horse is cool, and then the horse can be allowed to eat/drink.
