Welcome angiegarbe to irv2.
Is the wood only rotten around the hinge area?
If yes you can use a product that will patch the area and harden so holes will have to be drilled to place hinges.
The filler has material to prepare the wood before adding the filler.
Have used outside on windows and painted makes wood like new.
If its really rotten you will have to replace wood board and maybe could use the new plastic fiber boards you will find in Lowes or HD.