No offhand slot in horse inventory?

What I expected to happen was...:
when I opened the horses inventory I expected to see a shield for my offhand slot.

What actually happened was...:
I opened the horses inventory and all I saw was the main inventory.

Steps to Reproduce:
1. Tame a horse and saddle it
2. Get on the horse
3. Press "E" to open the inventory

Note:
I don't know if this is intended because you cant review armor placement either.