This is very controversial. You are probably not going to like my answer, so please don't kill the messenger! There will be more issues with ballet than there would be with modern dance. Dancers, like martial artists, have a low incidence of ACL injury. However, pointe shoes change the equation.
Back in college, I had a cutting-edge kinesiology teacher who used to argue with the dance students about the "pointe issue." Apparently, there are a number of problems associated with it that can be permanent. However, here is an interesting article about old vs. new style pointe shoes:http://www.gaynorminden.com/oldstyle.html
There are a few other issues. Some dancers get so used to working in turn out that they start doing that on the slopes, but that usually applies to new skiers. Also, many ballet teachers will try to discourage dancers from skiing.
In the end, it's a judgement call. Good luck with your decision.