No cover-up needed if you just want it to survive. If wife wants leaves un-burnt by frost then bring inside garage or cover Brian.
The mint thrives here without any over-wintering protection but dies back to twigs every fall, the regrows from spreading runners like strawberries in the spring. It seems extremely cold hardy as surprisingly do many succulents like your mint's neighbor.
Also spreads from seeds. It can get pretty invasive and you or your neighbors might regret my giving it to you if it escapes in your lush landscaping.Keep it caged in that cute pot and then you can more easily control its spread.
It looks really happy there as a color pot. A second pot could be made that would allow you to harvest from to make tea, mint juleps, mojitos, air freshener, decorate a lamb dish, etc without worry of damaging pretty pot's appearance and thus getting banned by Barbara to the garage and your TW collection.
P.S. It is supposedly good at repelling rabbits and other browsing critters, the mint oil is one of natures many chemical weapons. I love its appearance, flowers,taste, aroma, the way it chokes out invasive grasses, etc and would let it run wild here but it was deemed a weed by Mrs. Fred after it choked out one of her pretties. "Yes Dear, I'll weed out the mint right after I get back from my TW ride."