I have the Kubota insurance on my BX and the Kioti insurance on my CK. I cant remember the details for the Kioti, but the Kubota dealer told me it covers any damage to the machine no matter the reason. Car side swipes you while you're moving snow. The neighbor's cat decides to shred the seat. But I doubt it would provide any liability. That would be your homeowners.
But IIRC... Your homeowners may NOT cover the machine itself. It could be different in your state, but some homeowner's policies do not cover equipment worth more than $5k in certain scenarios. Ex. Using the equipment while not on your property, unit stored outside and either a tree falls on it or it is stolen; you might not be covered.
I'm guessing an inland marine policy would be needed for the machine itself. But as JeepHead said above, best to ask your agent. Provided your agent knows this kind of stuff. I've discovered most homeowners policies are for 'regular' people. The kind of people that don't have a personal shop, commercial lawn mowers, equipment, ATV's, or large collections of things.