Yes, but good wheels with good rims and hubs are more likely in the $200 range. There are $50 wheels on eBay, too.
He told that he wanted studded snow tires for the winter and street tires for the summer. I'm sure he will have flat tires in between, so he'll have to take off the tires anyway, a 5-minute process. Also, if he's took off the wheel to put another wheel, he's done 50% of the tire changing job.
By the way, good studded tires are expensive, Nokian for $50-70 each; and he will lose studs if he rides on the paved roads.
I would say that he needs 3 sets of wheels (or tires): studded - ice, knobby - show and mud, slicks - for the paved roads. Though, I suspect that for the city commuting some all-season semi-slicks will be OK:
http://www.sheldonbrown.com/brandt/ice.html
Ice riding is best done with studded tires of which there are a few suppliers, mainly in northern Europe, such as Nokian.
In the absence of studded tires for frozen lakes without a snow crust, slick tires are better than ones with miniature automobile tread because they give more contact surface, thereby reducing contact pressure and slip.