Ok, so I recently got Skyrim SE for the PS4. I have played Skyrim on my PS3 before. Anyway, on the PS3 version, you can fast travel to the College of Winterhold while on a horse, and it will put your horse (and you on it) on the bridge, near the front gate. However, when I try to do this on my PS4 version, it puts me on my horse up in the air to the side of the bridge (about 10 feet above the bridge and to the right), and my horse falls to the ground beside the sea below the bridge. My horse dies and I fall off of it, but I am barely hurt. I have lost 19000 gold because my horses kept dying when I would fast travel there, but it wasn't every time. Now, I no longer fast travel there, but it is really annoying because I don't have a house to put stuff in, so when I'm overburdened I go to the College to drop off stuff in the wardrobes there. I have to fast travel (on my horse, of course) to the actual town of Winterhold, then slowly walk to the college. Why does this happen to my horse? Has anyone else had this problem?
Based on this thread, it sounds like this has been a bug for years, but since I've found no evidence of a fix, it doesn't look like there has been one (yet).
I've heard that if you're on horseback and you fast travel to the College, there can be lethal consequences for you and/or your horse.
Yup, don't fast travel to the College on a horse. Sometimes you'll be fine but most times it'll load you up in the air over the chasm.
Basically, the solution is just don't fast travel to the College of Winterhold while on horseback if you value your horse's life.