I actually got this bug when i tried out the special edition.
I had no idea what the hell was happening, but i liked it. It was actually even more violent than this gif, cause our carriage got flipped upside down for the duration of the ride.
Even now, Skyrim’s intro is a delicate little flower. If you have a lot of mods, you’d better hope you have a way to load those mods before you go into the intro, because you never know what’s going to upset it. Even if it doesn’t go wild, you can have things like horses leading the carts into buildings and being stuck forever.
That would explain the game at launch. That doesn't explain the re-releases on previous gen (whatever that edition was called - super-duper-ultimate Skyrim or something) that still contains many of the same bugs.