Most/all wheels have a urethane or similar coating, so there should be no problem.
That said, if you are going to be changing tires twice a year, having the extra set of wheels makes sense. If you have to have the tires remounted twice a year, there is a chance of damage. Plus, you would need to have them balanced each time. No, that wouldn't make up for the cost of the new wheels, but not having to mount and balance does reduce the net impact on your wallet. Plus, since you do have this concern, having 'winter wheels' will give you peace of mind.
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