It doesn't have the highest ground clearance, but it should be able to handle 6 inches of snow, or so. You will certainly want to get some good winter tires. Check with others as to if they use studded tires as well.

My 2005 Matrix doesn't have much more clearance, but I have plowed through a good bit with it, though it is AWD.

As the fit is an econo box, I would suggest insulating it some. You can do the insides of the doors, that will provide some extra warmth, and sound deadening, and so the car is quieter while at speed. You might be able to do they roof some, and the floor as well, though I have never tried either.

Make sure to get some winter wipers, some good windshield washer fluid, keep an extra jug in the car, and a good winter kit, just in case.

You didn't say what year you have, but overall they are very reliable cars.