In the process of testing my mod (Dude! Where's my Horse?)'s compatibility with your lovely mod, I've managed to encounter a client-side NPE while shift-clicking a saddle onto a reindeer while riding it.
I've been testing with your mobs for quite a long time today and part of the process involves shift-clicking the saddle to ensure that they're properly registered with my mob as targets for summoning.
The reindeer appears to be the only creature that this error occurs with. I thought it was consistent as it happened earlier today on my first attempt, and then again just now on my first attempt after saddling all other entities, but upon having to restart my server due to some networking issues, as well as the client, I'm no longer able to produce it reliably.
While there are a number of other mods installed in this mini-pack for testing purposes, I don't believe that any of them would interfere with entity inventories (at least not for entities outside of their pack).
The relevant crash logs are: https://gist.github.com/duely/3f3f73afea719f15928b92f25e6da3f2
From what I can make out, it chains from your interface code into Container::slotClick. My decompiled version of Minecraft is obviously using different line numberings to the actual crash reports, but it would appear that same call to return an ItemStack is returning a null.
Apologies for not giving much information, but thank you for sanely implementing horses that actually derive from AbstractHorse!