As a fellow Minnesotan I can give you some winter recommendations that may be useful but winter riding conditions vary so much, even over the course of single commute, that it's hard to talk in absolutes. There's quite a few people, who ride mostly in downtown area of Minneapolis, that stick to skinny slicks during the winter finding that they are better at cutting through the slop to get to a solid surface. In my experience that might work OK when the roads are cleared pretty quickly and are well traveled. It doesn't work so well when the snow piles up and there's lots of ice.
If where you ride you encounter a lot of ice, studded tires are the way to go. In my opinion any studded tire less than 35mm is worthless. I know you said you can take cyclocross width tires on your bike but 35mm tires plus fenders (which you're really going to want in the winter) might be pushing it clearance wise for some cross bikes. I ride on 40 mm tires for the worst parts of the winter.
Anyway, there's a winter forum with some stickies that might be useful. There's not a lot of posting going on this time of year. There's also a site called "icebike' or something like that which has a lot of good info but hasn't been updated in a long while.
You've already gotten lots of advice on wheels so I won't go too much into that. My guess is the problem with your current wheels is that they weren't tensioned properly in the first place which is a common problem with inexpensive factory built wheels. Unless you're a bigger guy or carry a lot of stuff (which you might), you don't need to go super crazy on the number of spokes. It doesn't really hurt anything if you do since you don't race (I'm assuming). Since you're going to be riding in the winter I'd be sure to pay attention to the hubs and make sure you get ones with bearings that are sealed well.
I'm not recommending low spoke count wheels in your case but quality, hand built ones, especially with aero rims can be pretty tough. I have a set I got for group rides and triathlons but in practice I end up commuting on them quite a bit too because I'm too lazy to switch them out. I've hit some bad pot holes and I go off curbs with them (not at 20 mph or anything) and they're still true. The roads on our normal group ride route are pretty good but there's a couple of places where they're awful. Most people who race put ridiculous amounts of miles on their bikes and most are amateurs who don't have people handing them a new set of wheels if something breaks. The caveat is that most people who race aren't overweight and don't carry any extra stuff with them. Again, I'm not recommending low spoke count wheels but I thought I'd put in my 2 cents about them since I think they're often considered more fragile than they really are (good ones anyway).