The pass is the ticket
Window lift tickets for a family of four can exceed lodging. Epic and Ikon, bought in spring, are how normal people ski more than a weekend. Do the math with the number of days you will actually ski — not the number you fantasize about while looking at a map.
Kitchen > village plaza
Breakfast and at least one dinner in the unit. On-mountain lunch is the remaining tax. A $18 grilled cheese, times four, times five days, is a used pair of kids' skis.
Pick the unfashionable mountain
Brighton instead of Park City. Winter Park instead of Vail. Keystone instead of Breck if the kids are little. Okemo midweek instead of Saturday. Same snow-ish, different invoice.
Don't cheap out on ski school
This is the one line item I will not tell you to cut. A bad first week is how you fund ten years of 'they didn't like it.' Cut lodging prestige. Cut the tram lunch. Book the lesson.