I wouldn't let the weather deter you from applying to a good program just because your father said so. It is a consideration, if you're going to be miserable there, but just because your father doesn't like it doesn't mean you won't like it. When I lived in MI, one of our grad students was from southern CA, and the furthest north she had lived was in Davis. She enjoyed the snow and cold a whole heck of a lot more than I did, took up cross-country skiing, even got so carried away with snow shoveling that she shoveled the sidewalks for her entire block (she usually ran several miles every day, so the snow and ice on the ground seemed to leave her with quite an excess of energy she needed to burn off...I'm sure the neighbors didn't mind, I just wish I had known to live next to her!)
As scorpa said, just buy a really warm jacket (and hats, gloves, scarves, snow boots).
When you narrow your list by academics, you should visit the schools anyway. How will you know if you like any of them if you don't visit? If you're really concerned, visit in winter and see if it'll be absolutely awful to bear or if you can tolerate it (and keep in mind that it will be the ugliest time of year to see the campus, so you'll really see it at the worst it can get).