Summary: While equipped with a saddle/carpet rendering of each is inconsistent between mobs. Camel, Donkey, Horse, Mule, Skeleton Horse, Zombie Horse are 100% invisible. While the Llama, Pig, Strider, Trader Llama have their Saddle/Carpet rendered while invisible.

Steps to Reproduce:

1. Summon the following with no AI, tamed, and saddle/carpet/chest equipped:

• Camel
• Donkey
• Horse
• Llama
• Mule
• Pig
• Skeleton Horse
• Strider
• Trader Llama
• Zombie Horse

2. Apply invisibility effect to all entities via

 /effect give @e minecraft:invisibility infinite 1 true

3. Observe inconsistencies between mobs as to what is rendered invisible, and what is rendered visible.

While similar bugs have been reported, I wasn't able to find any that contained a direct comparison of all player mountable mobs with images as provided here.

Thank you for your continued help!