I've been coordinating a trip for 4-7 people for the last 7 winters. I might suggest find a few more people because some of the costs like lodging and rental cars cost the same whether you have 2 or 4 people.
We did a week in UT last year including 7 days on the mountains for about $1200 all inclusive, and we weren't really slumming it.
I fly Southwest almost exclusively, they don't charge you extra for your snowboard, or checked bags, they have low airfares and they fly in to most of the places you need to be, like Denver, SLC, Reno, etc. The only time I've ever paid more than $300 R/T for airfare out west was when we went to Jackson Hole (Southwest doesn't fly there).
Although you might find some cheaper, plan on $70 each way for shuttle service. Usually in the range of $50 to 100.
if you're not using a shuttle or public transit, car rental is going to cost you $50/day for a car or $100 per day for an SUV 4x4.
$50 to $100 per day. Do some research online and find out you can get discounts buying them in advance, via Costco, or certain shops, etc. Multi-day passes save some cash, too.
Of course if you have to stay at the Marriott slopeside, you're going to pay $800 per night.
You can get a no-frills hotel room for $100 per night in SLC for example, about 30-40 mins from a lot of mountains. Obviously lodging options are more limited (and more expensive) the closer you get to the mountain and further you get from a big city. We had good luck last year using VRBO.com
for short-term rental houses/condos.
We have usually been able to find condos near the resorts for about $200-250 per night which accommodate 4+ people. If you go off-peak, you can usually get better rates.
You can easily get by on $20/day if you prepare all your own meals. Probably closer to $40-50 if you're eating out a lot. We typically have a few nice dinners out at a brewpub or decent resto. Other than that we buy our own groceries for lunches, breakfasts, snacks, etc., and avoid eating at the resort at all costs (unless you like $14 hamburgers).
Resort bars are expensive. figure $50/night out maybe.