Prices are going to be all over the map depending on the choices you make. Many people in your position get at least a part time job to get access to discounts on skiing/gear/food/lodging.
Top end gear is about $2000 US list price (all my prices US), Figure about 1/2 of that if you find a good sale on last years gear. Figure about 2/3 of that for intermediate gear instead of top end gear. Figure about 1/2 of that for good used gear. So gear should run from $300-$700.
Cheap housing is probably going to range from $10/night to $30/night depending on where you go, what space/deals you can find and what conditions are acceptable. At Park City this last season, employee housing could be had for $12/night (including bus service to/from the resort). Last season I rented a room in a house for about $600/month that was about a 30 minute drive from the resort.
Season passes typically range from $400-$2000. My pass was free because of my job.
Food costs can easily range from $5-$40/day depending on how much ramen noodles you can stand to how much resort food you pay for. Food (including alcohol) for me was about $15/day, but most of my lunches were either paid for or subsidized (via work) and I ate at restaurants maybe once/week.
Transportation costs are all over the map depending on travel from home to resort and what kind of transportation you use at the resort. Many places have good enough free bus service to get by without your own transport. I used my own car, but bought studded snow tires ($600). Gas for the season was about $200. Round trip travel from home to resort was about $500 (hotels/food/gas).
Add miscellaneous expenses to your budget. I spent money on extra gear (hats, hand warmers), gifts for friends/bribes for bartering, and extra crap (shovel, anti freeze for the car, non-slip mats for a walkway), surprises (snow blower repair), laundry, etc. I figure I spent about $100/month, but I splurged. $25-$50/month is safer.
All in all I figure I got around 95 out of 120 days on snow working a full time job and netted about $10K after expenses. But most of my days on snow were spent working (i.e. teaching) and I only did this well because I am a certified instructor with a lot of experience. Entry level people are lucky to break even. People working part time on off slope jobs are lucky to get 3-4 days/week. Beginners not working are lucky to get 6 out 7 days on snow just for injury/sickness/stamina/weather reasons. Without working, doing a 6 month season for under $10K is probably doable if you're really frugal. If I wasn't working I could have easily spent $15K-$20K living in Salt Lake, Utah and skiing for 6 months.
Don't under estimate how physically tiring skiing every day can be. With your experience level, you could get worn out well before 6 months. The last thing you want to do is get injured because you tried to push things too hard. On the other hand, young people can often do amazing things. Good luck!