Hey, winter is for winter sports. I know a lot of folks like riding trails with knobby studded tires, but winter is for skiing, not bike riding!

A large piece of cardboard provides plenty of protection for the drips of oil coming off a bike you're working on. I've found flattened bike boxes to be excellent = they are large and thick. Tape w/ duct tape if you combine pieces. Buy an inexpensive repair stand or look on line for a plan to make one. It is just about essential for doing serious work on a bike.

As for your question - if you have an interest, modest aptitude and some tools, get a good bike repair book and tear it completely down to the ball bearings and put it back together. It is actually pretty simple mechanics and can be a lot of fun if you have the time and inclination. there is no harm doing it, especially if you can admit you need help if you have problems and can afford to take it into the LBS to get it. Make sure you don't lose parts!

As for what to do - why not call an LBS and find out what they recommend for things such as the "minor" and "major" tune up they do? At the least you want to inspect everything and repack hubs, bottom bracket, head set if they are gritty or not smooth. Me, if they feel good, I don't bother unless I just want to do it for "fun".

Remove chain and clean thoroughly, rinse and re-lube. Get a "quick link" installed if you don't already have one rather than hassle with the fussy pins they have nowadays.

Clean and oil any moving derailler and brake parts. Lube cables and replace if they aren't smooth and unrestricted. Clean and polish bike, sprockets and wheels if you're so inclined..