I hit Snowbird on June 4. Conditions were nice near the top of the Tram; Upper Chips and Silver Fox were quite good all day. Same with Regulator Johnson and the Road to Provo. If you want a treat, go through the Forest Service warning gates and hit Last Choice.
The lower parts of the mountain, below Rothman Way, were quite sticky and slow, especially in the afternoon. Coverage gets a little thin, but you shouldn't have any problems getting to the Tram base.