Winter Cycling - New (used) frame and fork for winter bike

I just picked up a frame and fork for an older Trek 700 Multitrack and want to build a multipurpose bike that will be a trail/beater in the summer as well as becoming my winter bike once the snow flies.

It's a 700c frame with 132.5 dropout spacing and frame clearances similar to a MTB. I've got most of the components that I will use for the build already but what I'm wondering about is wheels. The wheels I have is a mismatched set of 36-spoke factory built rims. I don't know the exact width but they currently have 700c x 45 tires on them and it doesn't look like they'd take anything substantially wider.

Is a 45mm studded tire going to be a decent arrangement for riding winter trails and icy roads, or do I need to look for wider rims?

that's a big maybe and it depends on the quantity and consistency of the snow.
45mm is a decent size, however.
some of the fatter ones come in 1.9" and 2.1", which is around 48mm and 54mm, respectively.

I rode nearly all of the winter last year without any studs at all , just some old knobbly 27 x 1/3 's. I took one minor spill , and that was because I haphazardly used my front brake on an icy incline. I would say you'll do just fine, Minnesota is comparable to Winnipeg in temp / snow levels and I imagine the city does an OK job clearing the major roads.

Actually I'm in a small rural town and snow removal is hit and miss. Of more concern that the depth of snow is the uneven ice that builds up when a poorly cleared road gets slushy, then freezes with lots of wheel tracks and other assorted bumps and ruts. You can end up with a slick, smooth, but uneven surface that makes keeping a straight line almost impossible and can suddenly sent either wheel sideways several inches. I'm hoping the studded tires will help with the ice and that the size will be appropriate for at least a few inches of slush or snow.

I would go with a 40x700 Schwalbe Marathon Winter tire or the 40x700 Nokian Hakkapeliitta W240. Both of these designs include plenty of studs, both in the center as well as the sides of the tread to help give you grip in all icy conditions. When the tire gets into a rut, the studs on the side can dig into the ice and you remain in control. If your tire only has studs in the center, it can slide along the side of a rut, and never climb out.

The 700x40 size will also provide enough clearance for ice and grit and allow fenders.

I'm using a set of 40 spoke Velocity Dyad & Formula hub wheelset that I found here: http://stores.ebay.com/Rocky-Mountain-Cyclery/Wheel-Sets-/_i.html?_fsub=1381074013&_sid=45396323&_trksid=p4634.c0.m322

I paid less than $150 for the wheelset and am happy with the super strong quality.