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Sorry to hear but you should be OK.
Just uncovered my Montauk 150 which had a full cover (engine included) and was in unheated dry storage. No rodent problem. I did clean the boat very well before putting in storage and a couple of sheets of Bounce.
Ran her this weekend and all was good.
I have tried many different ways to keep rodents out of all my boats offer the years and nothing really works but I always try something like mothballs, dryer sheets, traps, etc. Sometimes you get lucky and sometimes you don't.
Traps outside seem to be the best solution and nothing that they can use to climb on board.