It's not a good idea to cycle on the sidewalk from a safety perspective. If the busy road you're talking about has sharrows, it's already designed for biking. Make sure that you have proper lights/reflectors front and back on your bike and wear a bright jacket with reflective stuff on it.
I do a lot of biking in the winter. With any winter bike you need to oil the chain very regularly, check the brakes/pads on a regular basis, and rinse off the salt after a wet ride. It's worth greasing your hubs, seatpost, and any bolt that is threaded into the frame once a year to prevent water intrusion and frame rust. A fixed gear bike is going to be slightly easier to maintain (you don't have to worry about greasing cable housings and putting a drop of oil on the derailleurs from time to time), but it's not significantly harder to maintain a bike with shifters.
I use rim brakes on my winter bike, but would prefer discs. They just work better in slushy conditions. Better brakes are safer brakes. Studded tires are only really necessary if you bike on ice regularly. They really suck on plowed roads. Around here the plows and salters get out early enough that icy roads are rarely a concern . . . and skinny road tires with a little tread on them work well in snow and slush (completely smooth tires don't grip well in snow in my experience). If you're going to spend money on tires, get flat protection. It sucks changing your tube out with cold fingers on the side of the road in the dark at -15.