Compared to a Subaru any FWD car will feel like crap. My parents have had 3 and I love driving them in snow.
You need to take it slow -- go *very* slow on the gas pedal. Spinning the tires gets you no traction and is a great way to waste fuel.
The tires make a huge difference of course - quality, tread (very important), and type of tire.
Have you ever seen the movie Cars? "Turn right to go left ... yeah right old timer!" I often slide around a corner

and then turn the wheels to compensate. That way you don't spin out.
If you are traveling forward and do start to slide, you can point your tires in the right direction and blip the throttle a bit instead of stomping on the brakes. Since it's a FWD car, the tires will spin toward where you want to go.
If you can find a disused parking lot, I'm sure you can practice some and get used to how your new car feels in the snow. There's no denying that AWD is better (I'm a Subaru fan myself), but the Contour is a great car in the snow compared to many other FWD vehicles.
Be thankful now that you didn't get a RWD Volvo wagon