No, The surge protector is to protect whatever is plugged into it from electrical power surges that may happen, for example, if your house gets hit by lightening. The GFI, if it senses a big short, like an electrical device dropped into a bath tub, will immediately cut off power from the outlet.
Usually the outlets on the outside of your house, are either going to be GFI outlets, or the outside outlets are going to be protected with an GFI breaker, in your house's electrical panel. If that's not the case, them what you have is VERY dangerous. Unplug it. I would not even want to put something like the cookie tin heater outside and exposed to the weather. My fount warmer is in the coop, where it is protected from the weather.