I am from Seattle, so I am a dampness expert.
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You already have the cover, so absolutely use it. Just make sure the bike is fully dry before covering it. A cover does more than keep water off. It will keep off dust and whatever flies around in the air in your garage. Like... if you're using the garage for projects, creating sawdust and such.
Damp air is still damp whether you cover the bike or not, and even if it were heated. Our house is plenty warm but we'll get mold in the corners of the house if we aren't vigilant (behind water heater, in closets, etc. The bike should be fine for a few months so long as you put her away dry. And of course you can always take the cover off at the new year and check her out.