[Saintlysins]

You’re welcome Garrison. I may have read your concern wrong, so I’ll address it this way:
“when the frost comes out of the ground in the spring, my garage floor gets damp for a few days. I don't know if it is coming up through the floor from below, or it it is moisture that may have settled in right before it freezes in the fall”
Water does not ‘settle in’ or maintain a presence waiting for thaw. Unless there’s moisture getting on the “surface” of the floor from above somehow (water flows in from the outside) … then it’s migrating up from below … which is thee reason to NOT put down tiles with mastic.
If you’ve got moisture issues (not to rain on your garage dreams here, but it sounds like you do), you’re better off putting down an Indoor/Outdoor tile. Winter freeze/thaw and any other moisture issues will pop any tiles put down with mastic and grout. Without getting into French Drains & Sump Pumps for cure of your garage slab and water table issues, it seems the best solution for your situation would be going with the plastic tiles. The one’s “CheapShot” put in his post would NOT be a good solution for you as they will trap moisture vapor underneath in their ‘grid’ supports, which will support mold & mildew. There are tiles that are ‘webbed’ or ‘breathable grid’ style and far more suitable to your situation as posted by “Holland Patrick”.
I am quite confident in my answers as my former career was in commercial flooring and I only want to be helpful, I say all this with one GIGANTIC DISCLAIMER … my answers are solely based by my interpretation to your post regarding moisture and I don't want anyone to spend good money without doing the proper prep and test first. (Do I sound like the side-labels of our detailing products or what?)