Sure. But in my experience, even having 2 wheel sets for one bike is less of a benefit than you’d think it is. It’s not difficult to swap wheels but it’s a lot less convenient in practice than it is on paper. You have to do a lot of planning before hand and that takes a lot of the spontaneity of riding out of the equation.

I mount studs to my spare wheel set but I generally leave them on one bike during the winter so that the bike is just ready to go. I don’t do a lot of switching back and forth because it’s just a hassle.

Your idea would require removing wheels from one bike, setting the bike aside, removing the wheels from the other bike and putting them on the first bike, then putting wheels on the second bike so that it’s not just laying around without wheels. By the time you are done swapping wheels, the desire to just go for a ride has passed.