Hi there,
If you're definitely going to have to deal with snow, slush and ice, don't get a road bike, in my opinion. They're great, even in the wet, but if you need to withstand a few crashes (which I'd assume likely in these conditions) get something tougher. If you're route isn't really hilly, weight shouldn't be too much of an issue, and with an UAB or MTB you can get out of trouble quickly by jumping on/off the pavement in a crisis. You also don't need to worry too much about submerged potholes under snow and you can get out of trouble fast by jumping on/off the sidewalk. I fell down a flight of stairs with my cheapo Jeep Liberty full sus bike and it upended and landed on me and the concrete from about 3 feet up and I limped away needing no repairs. That wouldn't happen with an affordable roadbike I don't think. Just my 2 cents