The plastic fasteners on modern toilet seats don't corrode. But most old toilet seats are held in place with metal bolts that tend to rust in place over time, making them impossible to remove with a wrench. That leaves just one option: cut the seat off with a hacksaw.
First, protect the top of the toilet with strips of duct tape or thin cardboard. Then use a close-quarter hacksaw like the one shown above to cut through the bolts. If you don't have this type of saw, remove the blade from a standard hacksaw and use it by itself to cut through the rusted bolts.