Most hybrids have decent clearance for medium-wide tires, like 700x32 to 700x40, even with fenders.

One solution would be to winterize your bike with full fenders and even with a home-made mudflap to lenghten the front fender and protect your shoes and bottom bracket.

Then, depending on the roads you are and their condition, as well as your level of confidence, you have three options.

1. Use the bike as is.
It works fine in fresh snow (tires cut through it), but that's not a good overall solution.

2. Use cyclocross (aka knobby) tires
If you get some with a smooth centerline, you get the best of both worlds: a relatively smooth and easy ride on pavement, and sculptures that grip in the snow.

3. Use one or two studded tires.
For commuting, the front studded tire improves riding on ice, uneven packed snow and other similar conditions. A rear studded tire adds a bit of traction, but not that much, unless you ride off road.

My solution is to put two cyclocross tires for Winter, and to get an extra front wheel (used, $20) on which I install a studded tire on it (Innova 700x35). When there is snow or icing rain, I install that front wheel on the bike.

If you don't feel confident about your riding skills in Winter, it's OK to stop. If you check weather patterns, you'll find that there usually are quite a few warm days in December and that, when we reach February and March, there also are long periods when the weather is quite interesting and when there isn't any snow on the road.

Regards,