I think my stove fan is letting in too much cold air in the winter and too much hot air in the summer.?

Yes because your question doesn't make much sense .

If your talking about the damper not closing all way then that would be a problem when the stove is not in use.

The fan has nothing to do with letting co.d air in unless you have a power induced fan for tne combustion chamber which are usually just found on high effluence furnaces which suck in air from outside into the combustion chamber and then vent directly outside.

Wood stoves would have nothing like be this .

Go get a pro

Guessing your talking about a kitchen exhaust vent over your kitchen stove. The backdraft damper could be stuck open but it may be that you have a negative pressure in the home that is causing it. Most of those backdraft dampers are not a 100 percent closure and will allow some air by. If so you may benefit from an air exchanger that would balance the air in the home. A good heating and cooling specialist is who you may need.

Anyone that can LOOK at where the vent exists the building should be able to diagnose the issue. A professional is overqualified, and will charge accordingly.