Horses a liability on a rural SFR property?

[Donnie Mac]

We currently have a rural home (our very first rental) listed for rent in Ozarks, MO and have had some interest from some potential tenants that own horses.  There are 12-acres attached to the property that are not currently utilized.  We have no issues with the horses on the property, but are wondering if there is any concern over liability if the horses get loose and damage others property, get hit by a car, etc.  We would leave the securing/reinforcing of the fence up to the tenants.  We are going to call our insurance agent to discuss, but thought we would get anyone's first-hand account if possible.

• What is our liability (if any)?
• Can we require that the tenants carry extra insurance?
• Is this type of coverage even available for renter's insurance?