It depends on what the beater bike is like. If you have a sturdy utilitarian bike in the first place, I'd go for winter wheels, great way to go when conditions change rapidly. If the roads are salted where you live, and if you ride through slush regularly, and especially if you don't have access to a warm, indoor place to wash off your bike regularly and tinker with it, winter conditions are too harsh for a lovely lightweight bike with expensive components. I've read that one winter equals 4 to 5 summers in wear and tear, and I believe it.

I wouldn't buy a beater bike if it's heavy or hard to maintain. Snow and cold and studded tires make it more than hard enough to ride already.