It's a simple equation of proximity vs. quality of accomodations vs. cost.
For example, you could live in employee housing (inquire with the resort HR department.) In that case, proximity is good, cost is low, but the quality tends to be poor.
You could also live off the resort in town - for example, Frisco, Steamboat, or Vail. Proximity is good, quality is good, but the cost tends to be high.
You could also live in one of the nearby communities, such as Eagle or Leadville and deal with the 45+ minute drive. Quality is good, cost is ok, but proximity sucks.
Finding the fabled "cheap housing" really doesn't exist, and almost certainly not for you since you're not a local. If you spend a few years there, eventually you might find someone who'll cut you a deal ($500 /mo, inc utilities for your own room would be a decent deal).
Thinking out-of-the-box idea: go to the trailer park in Summit Cove, find a trailer for sale, and offer the owner a ridiculously low price - like $2000 - $3000. Buy the trailer through a straight DMV title transfer and then abandon it at the end of the season. I bet there's some people very desperate to sell their trailers for any amount of $$$. Don't forget there's a monthly lot fee.