You - and everyone else that has posted here is wrong - please read:
1. This lawsuit was brought by Rick Alden and Bjorn Leines (Rick Alden started Skullcandy, Bjorn is one of the bigger names in snowboarding) - meaning this lawsuit has a LOT of money behind it.
2. Even though Alta is not a government actor, this group of snowboarders is trying to make an argument that the government is sufficiently entangled with a private actor so as to make the private actor a quasi-government actor - meaning that the private actor (Alta & its management) would be held to the same standard as a government actor. This is not an extremely difficult argument to make because 80%+ of the land that Alta operates on is US Forest Service Land. Additionally, Alta pays a percentage of its profits every year to the US Forest Service and the US Forest Service has to approve of Alta's operating plan every single year. Of course, all of this won't ensure that Alta will be viewed as a government actor - but this lawsuit was also brought against the head of the Forest Service.
3. If the court finds that Alta should be held the same standard as a government actor, there exist three different levels of analysis that the court can use in order to analyze the actions of Alta and the USFS.
You stated that they can't bring this suit because snowboarders are not a protected class... that is absolutely wrong. Anyone can bring suit against a government actor for discrimination...however... if the class being discriminated against falls into a protected class, the court will use a much more strict analysis regarding the reasons for that discrimination.
a. IF Alta were discriminating against a protected class (e.g. race, national origin, religion, alienage, etc.) then Alta and the USFS would have to show that the challenged discrimination and classification serve a compelling government interest and that the discrimination is necessary to serve that government interest. I.E. if the government is discriminating against a protected class, it is most likely going to lose.
b. IF Alta were discriminating against a quasi-protected class (e.g. gender, age, etc.) then Alta and the USFS would have to show that the challenged discrimination and classification serve an important government interest and that the discrimination is substantially related to serving that interest. I.E. these can go back and forth and either party could win.
c. THIS ONE IS MOST IMPORTANT. Because Snowboarders don't fall within any protected or quasi-protected class, then it will be up to Rick and Bjorn and their group to show that there is not a rational reason for the discriminatory behavior that leads to a legitimate government interest. Courts are usually pretty relaxed about what constitutes a rational basis, and are even willing to accept a rational reason that was not originally stated when the discrimination first occurred. So all Alta will really need to argue here is that they have this procedure in place in order to increase profits and customer satisfaction - and since that increases profits for the USFS, then that is rationally related to that legitimate government interest. I.E. if the government is discriminating against an unprotected class, the government ALMOST always wins.
Of course none of the above even matters if Alta just makes the claim that they are not discriminating against "Snowboarders" but are only restricting the types of products that may be used at their resort (i.e. they allow skis, but they do not allow snowboards, sleds, tobbagons, saucers, snowskates, tubes, cardboard boxes, etc.)