I’m an insurance agent, albeit more on the commercial P & C side than equine-related policies. Individual liability is common. The boarding barn carries their own liability insurance. ( If you happen across one that does not, run for the hills.) While the damages caused by your horse may technically be covered under their liability policy, carrying individual liability with them named as an Other Insured usually affords you benefits like defense costs & money to partially cover lost wages if you’re forced to take off work to go to court.
A word of warning: the Clanter fam has a rare jewel of a carrier and they should kiss their hands as a token of their gratitude. Some Homeowners policies only cover pets and consider horses livestock. Most Homeowners policies won’t cover damages caused by your horse off property. I.e.: I keep my horses at home. My 3yo WB, Fireball, escapes after a tree falls on my fence at 2am. He gallops onto the nearby Interstate & causes an accident in which a driver sustains serious injuries. So long as my Homeowners covers my horses, I’d typically be covered in this scenario.
Now, say I trailer my 4yo quarter horse, Lightening McQueen, out to a National Park for a trail ride. Lightening gets stung by a bee & throws me. He gallops out onto the Interstate & causes a car wreck. My Homeowners policy won’t cover this. Nor will they typically cover horses I compete or use for commercial purposes. Even if they’re kept at home. While there may be a Homeowners carrier out there that covers you for damages caused by your horse that lives at a boarding barn, I’ve yet to run across such a carrier.
Individual liability insurance is cheap. The USEF offers it to members at a group rate, iirc.