All season tires are more about traction in cold weather than they are about snow, despite the M&S on the sidewall.
That said, if you don't plan to really push the car they are a good all-around choice as manufacturers have really been pushing the envelope on these. The newest crop can complete with summer tires in the dry and wet.
Here are my low cost All-Season recommendations:
General G-MAX AS-03: I know a number of folks who run on these and LOVE them. Very good dry, good wet, and OK in snow.
Kumho Ecsta 4X My brother recently put these on his E55. Fantastic dry, decent wet, and work OK in snow.
Goodyear Eagle GT I drove on these for a year and a half and found them to be very competent in every condition. Though I suspect they would not match the performance of the tires above and am not certain they will come in your size.
The Michelin Pilot Sport A/S 3 is currently Tire rack's highest rated all-season tire.
And while I would likely agree, at $50-$60 more per tire, they damn well better be!
Tire rack has done a couple of tests of All Season Tire tests in snow:
http://www.tirerack.com/tires/tests/tes ... p?ttid=173
(Firestone Firehawk Wide Oval AS, General G-MAX AS-03, Goodyear Eagle Sport All-Season, Hankook Ventus S1 noble)
http://www.tirerack.com/tires/tests/tes ... p?ttid=177
(Bridgestone Potenza RE970AS, Continental ExtremeContact DWS, Goodyear Eagle F1 Asymmetric, Michelin Pilot Sport A/S 3)