I wish you guys luck, but I think it will be tough.
I am with a ski lease group in Mammoth. My wife and I, along with three other couples, rent a two bedroom condo from Nov 20 to May 20 every year. We have been doing it for several years, we know the owner well. He rents to other people during the summer. Most of the couples in our lease use the condo a couple of weekends a month, typical ski lease stuff. The condo is empty most of the time during the week, the landlord likes that because the wear and tear is low.
Mammoth is VERY low on long term housing from what I have heard. Our landlord picked us over lots of candidates, there is a serious shortage of long term housing because many owners would rather short term rent through airbnb. You guys coming in during February is going to be tough because most of the long term winter rentals will be taken by people who are renting for the whole winter, starting in November, you are coming in at a VERY bad time.
You will also have a tough time because owners won't want to rent to a large group, large groups cause more wear and tear in general.
You MIGHT be able to get a rental if someone wants to airbnb during December and January, to get the money, then rent to you from February through May, when there is less traffic. That will be tough, you might want to put out some adds out or contact a real estate agent. Contacting an agent might be your best bet, but they might well want your parents on as cosigners. One of the things our Mammoth landlord liked about our group is that we were all older and had real careers and owned homes, so we had some credibility in case things were damaged. At your age you won't really have that.
Ski town housing has always been tough, but now it is worse than ever. I really think you are going to have a tough time in Mammoth.
One of my first ski leases, after I left being a Tahoe ski bum, had a situation which might have worked for you. There were four bedrooms, each with four beds in it. The owner did it as a ski lease, then rented eight of the beds to a bunch of college students from Denmark. It was really crowded, but I was not going to complain because ski leases in Mammoth are tough to come by. The Danish kids left in late April, after being there two and a half months. This was more than a decade ago, I did not rent from the guy again and I don't have any way to contact him, even if I did I don't know if he is still doing this.
I think you might want to look for a different place, somewhere other than Mammoth. If not, you could try contacting real estate agents, that might be your best bet. You are coming in at the wrong time in a tough market. You would have an easier time coming in During November or December and staying the whole winter. Like someone suggested, Salt Lake, a place with lots more availability, might be a better option. Or Maybe try Bozeman Montana. I could be completely wrong, I don't REALLY know anything about Bozeman, but areas which are JUST ski towns might have more options for you. Ski town housing is tight, it is VERY tight when are trying to come in mid-season.
Reno might be another option. I realize it is not a ski town, but it will be easier to find places to live there.
Good luck.
People who have lived in Mammoth for years are having trouble with housing. It is simply a very tough market. We are really lucky to have the arrangement we do.