I get this too. Very weird that I can have it running for six hours while I sit across the room, no issues, but 5 minutes after I go to bed I apparently just stop stock still and sit for the night. I've also seen it a couple of times when I'm active near the PC: no connection drop or lag or 'bump' off path, the horse slows to a walk then continues to slow until it stops, like it got to the end of a pathing despite the looped path still being lit up.

Used to only find myself stopped the odd time, and it was always by a fence or wall just off my path (so obviously either lagged or bumped, sucks but unavoidable), but since about two weeks ago, it's constant, and always with me still perfectly positioned still on track, just the horse apparently decided not to go any more of its own volition. I've given up wasting longer duration scrolls and meals and whatnot unless I'm in the room or at least tabbed into another game so I can hit T again when horsey gets bored. Definitely something changed that's affecting it, so just have to wait for if/when that gets fixed.