The bug

Horses with saddle (does not matter whether tamed, Tame:1b) cannot be controlled by non-player mobs anymore. This used to be different in the past, at least in 1.13.2, but since about 1.14.4 the behavior changed.

However, horses without saddle can still be controlled.

How to reproduce

1. /summon horse ~ ~ ~ {Tame:1b,SaddleItem:{id:saddle,Count:1b},Passengers:[{id:husk}]}
   

2. Summon a villager
   The husk raises its arms and orientates correctly, but the horse does not move