If its not in writing in a contract, the landlord can't do anything about it. If they want to alter the contract to reflect a no-exotic pet rule, then they should have to give you the option of opting out of your contract without any penalties, or letting you keep your animals until your current contract is up. It could depend on your local laws though, so be sure to read up on landlord-tenant rights issues for your area.
I would ask them beforehand what their policy is, and ask for a copy of a contract to review prior to signing any agreements. Then follow that contract to the letter to make sure that they can't confiscate anything or evict you for having them. And ALWAYS make sure to keep at least one copy of the contract, so that you have something to show them (and possibly a court or judge) in case anything does come up.