What no one mentioned is, FNIS can mess this up hard. In my case, i fked the internet for solutions. I tried some rather difficult and complex ones but the results were negligible. so today, I installed a home mod. saw my horse hitched at the hitch point. noticed it being not animated, when i got up, i had no control (i mean i cant move it, neither it moves by itself. Its in the "T" state of FNIS if u ever heard of it). the problem was, I installed some creature mods, then ran into a load order and save game problem. So i had to disable every mod and run fnis to make my character move (else the "T" problem). so basically, FNIS didnt animate the Horse, which ultimately resulted in NO CART ANIMATION!!! BOOM!!! PROBLEM SOLVED!!!!