Tough call.
The mountains are a great place to get away from shit and just be out there doing your own thing and chilling with the closest homies. You don't have to answer your phone, think about work, or girl issues. If she's up there with you all the time then skiing's not longer an option to get away from that stuff. But then again, if she loves skiing as much as we all do and rips hard then she's probably chill and would be awesome to ride with. Nothing hotter than a steezy girl who rips. As someone else said, a girl who can keep up and likes skiing, but wouldn't want to tag along every time I go up would be sick.
A chill girl that doesn't ski, but understands the whole skiing lifestyle and accepts that I would choose skiing over her in many situations is probably ideal though. And no, I would not teach her to ski. Been there done that with a close family friend, and had I not known her since I was born things would not have gone so smoothly.
I'd rather have musical taste line up with a girl, and leave the mountains as my thing.