Invisible saddle when using invisibility potion on a horse, donkey or mule

The bug

When you splash invisibility on a horse, the saddle becomes invisible. When you do the same on a pig, the saddle stays visible. Note that this does not affect horse armor.

Splashing invisibility on a donkey or mule with a chest and/or saddle makes those equipped items invisible with the animal. This also affects saddled camels: MC-256469

Steps to Reproduce

1. Summon both a pig and a horse with a saddle:

   /summon minecraft:pig ~4 ~ ~ {NoAI:1b,Saddle:1b}
   /summon minecraft:horse ~2 ~ ~ {NoAI:1b,Tame:1b,SaddleItem:{id:"minecraft:saddle",Count:1b}}
   

2. Obtain a splash potion of invisibility and throw it at both entities.

Observed Behavior

Saddles on horses are not visible if horses have the invisibility effect, unlike pigs.

Expected Behavior

Saddles on horses would be visible when horses have the invisibility effect, just like the saddles of pigs are visible when they have the invisibility effect.