With a spair set of wheels and tires I bet it would work well, probably get a few years of wear out of those hex screws in your use. If you get a lot of snow, I would probably get a set of bar tires. Stud the top of the bars with the screws. That way you have the nice open, biting tread of the bars, plus the screws, to bite into the ice. Also with the bars, you would have a lot of rubber where the screws go it, so you would not have to worry about poking a hole.
Anouther idea for you. I have never heard anyone doing this to a tractor tire, but the 4wheelers do it all the time. Sipping. This it where you cut small slits in the tread to help gram on to the ice better. If you look at any one the new snow tires out there, you will get the idea of what I am talking about.