The local Utards will need to chime in as to who usually has discount day passes and where they are sold. I know I had no problems finding tickets inder $60 for Powder Mountain and Snobasin by Ogden. Snobasin was one of the main Olympic venues, it is a pretty good area.
If you ar e going to be stubborn about going to Snowbird that one is going to cost you. No way around it. So get tour rape kit out.
I do also believe that Park City and the Canyons still offer a free lift ticket for the day you arrive in Salt Lake. Google it. If your flight gets in by mid morning, it is not hard at all to get a half day in. Takes maybe 45 minutes to get to Park City from the airport. Of course a car will really help in that endeavour.