I'll never tell people they have to, but winter running can be really enjoyable. I committed this year to doing as much of my training outside through the Canadian winter as possible, and so far it's been a dream. I ran through the storm that ripped through Ontario right before Christmas and caught myself thinking that I wasn't sure how much worse conditions would have to be for me to stop having a good time.

Like the beginning of your comment, it ultimately comes down to gear. An ankle injury is a good reason to not push yourself running, but the weather need not be :)