So hikers should be allowed as well?
How about I walk my dog?
I have a degree with an emphasis in constitutional law, while I don't have legal precedent for my opinion, and my opinion is no more "valid" than any of yours, I think maybe I can offer a little more insight on the "constitutional rights" of protected classes.
Snowboarders in and of themselves are not protected classes, that's reserved for sex, religion, age, etc. But it doesn't mean that people aren't protected from discrimination.
But, I believe there is some sort of system the US government uses to determine what public lands can be used for. Such as certain land can be hiking only, or hiking and mountain biking. All the way up to something of the effect of Dirt Biking and ATV'ing, while prohibiting hikers from such land. Because its in the best interest of the safety of both parties involved.
So yes, they can open Alta up to snowboarders while still prohibiting hikers and such because of the risks involved with having two different types of recreational activities and the risks involved between having the two on the same land. The same can't be said for having snowboarders and skiers on the same land since both activities are so similar.
I should add that just because snowboarders are not a protected class, does not mean they don't have legal rights to not be discriminated against. Alta is going to have to prove why being skiier only is in the best interest for both parties involved. With 99.9999% of resorts being snowboarder/skier friendly. I think they are going to have a tough time proving it.
The other big issue is its tax payer funded. Hate to say it, but that's going to be the deal breaker for the skiers.