700x38C vs. 26x2.1 - I've been on both, and the 700C was definitely faster. I found that the narrower tread cut down through the soft snow to whatever hard surface was underneath [hard snow, ice, pavement]. When on bare pavement, the difference was even more profound. I found that the 26" tires were only superior when riding in frozen ruts and on steeper climbs.

As for the bike, if you can fit the studded tires onto your current ride, you might as well do it. Another option is to find a used mountain bike that uses disc brakes. If you want to use the stock 26" wheels, you're good to go. You could also rebuild the disc hubs to a 700C rim - there will be clearance on most mtn bike frames, even with fenders. In either case, sell/trade the suspension fork for a disc-compatible rigid fork and you will have a foul-weather machine par excellence.

Chains suffer mightily under a salty onslaught. Buy a better-quality chain with nickel plating to maximize life. I've used Finish Line Wet XC lube for quite some time with excellent results. Even if the chain does rust, adding more oil and then going for a quick spin gets it fixed right up. For the rest of the drivetrain, go singlespeed.