Lisa,
check my homeowners for liability insurance to make sure i'm covered that why.
I would bet dollars to donuts that the HO liability WILL NOT cover any horse-related claims. Or, they may possibly cover one if it is very small and inconsequential, and then promptly issue a cancellation for "increased risk" or something similar. (Heck, these days, most HO policies won't even cover claims from household pets, much less an animal that is considered livestock!)
As long as you have an Equine Liability policy, you should be ok. If you have a personal umbrella liability policy, you might see if they will offer excess limits over the primary equine liability limits, just to be safe.
Jill & Eli