My chick is decent enough at snowboarding to where she can at least keep up and not slow me down that much.  The trick is to bring your girlfriend AND one of her friends, so you can ditch her if you want to go shred the gnar for a little bit.
As for teaching a girl to ski, my rule of thumb for everyone learning is that they will hate the first day and never want to go again after the first ten minutes, but if you can get them back again they usually have fun on the second day.  Its funny, I've taught probably like 10 people to snowboard but I've never taught anyone to ski.  Even though I don't snowboard anymore really at all I find it easier to teach than skiing because I had to "learn" to snowboard, whereas with skiing I learned when I was so little its like it just happens and I'm not really aware of the technique going into it.