To register and insure a vehicle in Florida you will need to obtain a Florida driver's license. According to the FL Department of Highway Safety and Motor Vehicles - Canadian citizens are non-immigrants and are allowed to stay in the US without obtaining INS documentation. Canadians without INS documents must provide proof of Canadian citizenship to be issued a Florida driver license by presenting 2 of the following documents: Canadian passport, Canadian driver license, Original or certified Canadian birth certificate, Canadian Naturalization certificate.
As for obtaining car insurance, the mandatory liability insurance purchased in Florida is different than what is required in Ontario and because of this it would likely be difficult to find an insurance company that could cover your vehicle in both places. There is a Canadian Snowbird Association, snowbirds.org, which might be able to help you see if as a seasonal Florida resident you can obtain auto insurance for both Florida and Canada. You might also discuss this issue with your current Canadian auto insurance company.