To just steal a song you've heard in another video part is lame, you should put some effort into finding the music you're skiing too. IMO stealing a song from snowboarding is also lame, since they're very close. One thing that I have noticed though is nowadays some people just don't know that a song's been used before, since extreme sports and video parts have been around for a while now.
Using songs that have been used in other sports is a pretty common thing in skiing. Some would say it's an homage, sometimes it's straight up uninspired and copying. Cam Riley's part in Weight uses the same song as Heath Kirchart's part in This is Skateboarding. In this case it's well done, it's definitely an homage. Karl Fostvedt in All Damn Day, same intro song as Tom Penny/Arto Saari in Flip Sorry, also an homage. In those cases those were iconic skate video parts, so that's what makes it cool to reuse the song.
I'd say if you really like a certain edit, at least use a different song from the same artist. At least it shows some effort. Personnally, almost all the music/bands I listen to are from ski/skate/snowboard videos. I've stolen music from skate videos before to make edits, and I can think of one edit where it definitely was a great choice, the other ones I could've done better if I had listened to more music. This year I've put out a street video with my girlfriend, and both of our songs for our video parts are bands that I've discovered through video parts, and then I started to listen to albums from those bands and found songs that I really liked and used them for our video.