Find a heated car garage where you pay for a reserved spot (in Colorado it's like $100 a month). You'll have a semi warm bed (a heated garage in winter will be like 50-60F), save money from what you waste on a actual apartment or heating a van in the outside lots and you can't get towed.
Then just be stealthy when you get in and out. Some caretakers/garage monitors don't really like people living in the heated garage. Varies company to company.
I know about 3 people who do this in Aspen. They all agree that being stealthy or at least avoid peak times when people are going and coming just help avoid concerns of rich people. If you think about it I'd probably throw a fuss if I know the skibum who parks next to my $250,000 Mercedes lives there all the time.
I was also going to do this last season until I was made a live in caretaker with free housing.
Other things to consider when doing this is the height of your vehicle. Make sure it will fit if there is clearance level.
Read the contract very carefully. If there's nothing in it about living in your spot, don't be stupid and give them a reason like throwing a kegger in the garage. Or blabbing to everyone about how cheap you live in the garage. As you know in ski towns everyone spread word fast especially about cheap housing.
Consider getting a gym pass or gym punch card for showers and such.
All in all if you spent $300 a month for a gym pass and heated parking space that will be boat loads cheaper then a apartment.
And you know where you can find a pay for heated garage spots usually? Right at the resorts. 2 minute commute to the chairlift. Go hit a hundred days dude!