Haha! I've exercised in the dark for the winters of about 20 (aii!) years and do I have stories to tell!
To the first part of your question, safety is job one of course. When going for a run I wear light colored clothing with reflective gear and travel on very well-known paths, normally neighborhood roads and sidewalks. No headphones, ever, night or day, and lately, I've carried a cell phone, though its bouncing in my pocket annoys me. Oh, and I tend to vary my routes and times, just in case some nut is keeping tabs. As I've aged, I have discovered that the lights of on-coming cars really incapacitates me so I simply stop and step onto the grass, period. If the car stops too, I immediately start walking to the nearest occupied house and then stop to look at them. They usually move on at that point.
When horseback riding in the dark I must also consider my horse's safety (oh, and yes, riding IS great exercise and just grooming a muddy horse burns about 350 calories) so I wear a helmet and try to keep the workout simple as my horse is afraid of snake-like shadows (the shape of hooves on arena gravel). We walk around the farm roads and stop to listen to interesting sounds and trot when the mood is right and the moon is helping. Net result: he trusts me without question and is in great shape.
Weird stuff: Once when running (I'm 5' 4", proportionate weight) I came across another night runner loping in the opposite direction. He was over six feet tall and very thin. When he came into view under a street lamp I nearly screamed because he was a mummy! I'm totally serious. He was wrapped in a wide, dirty bandage from head to waist with a down vest thrown over his back, face and arms completely wrapped, the end of the bandage trailing off one arm. You can bet all that sprint training came in handy! Once home, I called the police and the cop said "Oh him, the Mummy Guy. We know him, he's harmless, ma'am. Creepy looking though."
Fear: I don't really worry about being out alone at night except when on horseback, but even then, someone knows where I've gone and when I should return. I try to remain aware and see myself as the hunter, not the hunted. Obviously, I don't go if the neighborhood is bad or unknown. When possible, it's great getting out there and enjoying the peace and quiet of the night! I suspect I've run my best times in the dark.
Hope this helps!