That's very unusual. Thank you very much for this description, I will try to reproduce and fix that.
By the way, it would be very helpful if you gave me a screenshot of what it looks like during the issue. Ideally, if you could record the whole process, that would be super useful.
I'm also interested to know what happens if you close the map (esc or X)
Also, does this only happen with the horse, or when you enter the map by road (from areas that are away from the town) too?