Not a bad vehicle at all, but if you're going to be in heavy snow, on a regular basis, I'd recommend something with all wheel drive, front wheel drive (what the matrix uses) is better than rear-wheel for snowy conditions, but both can lead to limited accelerative traction, and front wheel has another design flaw for snow...
The rear wheels do 3 things. Accelerate (gas), to get the car moving (doesn't happen in FWD vehicles). Grip laterally, for turning and handling. And finally, deceleration (Braking), that's 3 jobs, max.
The front wheels have a little more placed on them... Generally, the front wheels have an engine located directly overhead, adding to the weight on the tires, which is bad for most situations (although good for handling in the snow, because it "digs" the tires down a bit), but in most other situations, that's a bad thing... Here's why...
The front wheels do a little more work in a front wheel drive car than the rears do in a rear. Not only are they expected to roll, and hold lateral traction in a turn, they actually redirect the car, hold the transaxle (how power gets from the motor to the front wheels) and the engine, accelerate, decelerate, and, often, the front tires are of equal, or SMALLER size to the rear.
A loss of traction on a well-balanced rear wheel drive vehicle leads to what's called "light oversteer" or "light understeer", which means the vehicle's tail will drift out, or turning response will be greatly reduced because of lack of traction. A loss of traction in a front wheel drive vehicle that's not perfectly balanced (this includes the Matrix) results in extreme understeer (you turn wheel, car doesn't change direction), and also a juttering, slamming, super-bumpy-road feeling (the toyota matrix, and the toyota line in general is VERY good at minimizing that portion, but it still happens). With an All Wheel Drive car, you'll have both the front wheels pulling the car, and the rear wheels pushing the car, if you're a Toyota fan, many of their models are available with AWD, Subaru and Suzuki have many great AWD models, as do ford/mazda, and other manufacturers. If you live in a snowy climate, AWD is the way to go, shop around.