The bug

With the use of commands, it is (or was) possible to summon untamed horses with saddles equipped on them. However as of the latest 1.16 snapshot, saddles no longer render on untamed horses and the saddle will only render on tamed horses.

However, horse armor can still render on untamed horses.

How to reproduce

In 1.15.2

1.  /summon horse ~ ~ ~ {Tame:0b,SaddleItem:{id:saddle,Count:1b}} 

   Successfully summoned an untamed horse with a saddle

In 20w15a

1.  /summon horse ~ ~ ~ {Tame:0b,SaddleItem:{id:saddle,Count:1b}} 

   (Same command)
   The untamed horse is summoned but the saddle is not visible

2. Kill the horse
   The horse drops a saddle.