They will be happy to give you advice. Ask them for names of those they insure, so you can call and check out what they are telling you. Once you decide on the agent and policy, ask for the application. This will save you time and money as well as guarantee that your new horse will be insured for his trip to his new home. If you board, be sure to advise stable of your insurance company name, and 24 hour telephone.
Most policies require prior notice to insurance company of surgery or euthanasia.