By (almost) any means necessary.
You can run, you can wear snowshoes, and you can even even grab a crazy carpet or sled if you think it will help. While it's mostly running, you can choose any reasonable, non-mechanical form of travel. No skis though - ski racing is a whole other ball of wax.
Hook or Crook Ultra is hosted at Pass Powderkeg Ski Lodge in Blairmore. The course takes advantage of the long and diverse trail network in the surrounding area. You will get up into some alpine areas that are accessible, even in the snow (with some hard work).