The Boise airport is small, and you'll have to leave the concourse areas to claim your snowboard bag.
There are very few, if any, suitable places to "camp" outside of TSA secured areas. Most of this area is open and brightly lit with tile flooring. The possible exception might be the greeting area for arriving passengers just outside of security.
There are several budget hotels within short walking distance of the airport. Most offer free 24/7 shuttle. Google Maps will give you a good idea of what's available.
I agree with WWGuy. You could do it, but I wouldn't recommend it. The terminal is tiny. If you do decide to do it, I think the best place to try to sleep would be just outside of security where most people wait for those arriving. The chairs all have arm rests, but it is the darkest area in the terminal that I can think of off the top of my head.