I didn't find any bolts under my cockpit winch bases (my bases are solid blocks of wood). So for my boat there were 6 wood screws holding each winch in place. Some of the other commanders on this site used a hollow fiberglass winch base. These should have through bolts that can be cut if necessary and replaced with stainless fastners.
On the mast, my old bronze south coast winch is held on with 6 small machine screws tapped into the aluminum spar. the only way they are going to come out is with a drill, but since that winch works i'm going to leave it alone.
by the way there is no need to remove the winch base for cleaning and varnish. if you plan to use the winches you have, only the top section needs to come off for cleaning and grease. if the winch is stubborn a little heat will help with dis-assembly.