Donkeys, mules and undead horses cannot be saddled by right-clicking

The bug

Donkeys, mules, zombie horses and skeleton horses cannot be saddled by right-clicking on them with a saddle, but horses can. This is inconsistent.

How to reproduce

1. Summon a tamed horse

   /summon horse ~ ~ ~ {Tame:1}

2. Right-click on the horse while holding a saddle
   → ✔  The horse is equipped with a saddle

3. Summon a tamed donkey

   /summon donkey ~ ~ ~ {Tame:1}

4. Right-click on the donkey while holding a saddle
   → ❌  The donkey is not equipped with a saddle (its inventory is opened instead)

5. Summon a tamed zombie horse

   /summon zombie_horse ~ ~ ~ {Tame:1}

6. Right-click on the zombie horse while holding a saddle
   → ❌  The zombie horse is not equipped with a saddle (its inventory is opened instead)