The mod causes the armor from caverns and chasms to render weirdly on horses, their body doesn't appear to have any armour except for the head and legs

Upload the game log, mod list and a with/without ImmediatelyFast screenshot

latest.log

Here's my log, and a before and after photo.
Here are the mods downloaded for these:
. Blueprint
. Caverns and Chasms
. ImmediatelyFast (Only for the photo without the proper horse armour)

Can you retest this with the latest ImmediatelyFast version