Man, I don't know. You could definitely do the first pitch of Stairway still on Saturday. We did the first two pitches of Stairway and White Nightmare today. It was raining in the valley, snowing up there, but it was a wet snow.
White Nightmare is starting to get thinner in sections. I wouldn't get on it on Saturday....it was sounding pretty hollow and detached already. After a few days of warm weather and some rain, it'll be pretty risky.
I'd stick to the first pitch of Stairway and take a look at the second one if you're up there. It's similar to White Nightmare in a lot of ways (WI4, curtain), and it might still be in. I know some people did all 5 pitches today, but the 3rd has a crack across it that might be ugly by next Saturday.
As for other climbs....
Bridal Veil Right is probably thicker than White Nightmare, but I think its getting a lot of water spray and that's affecting the ice. Might have to look further afield....Joe's Valley or Santaquin (if avy conditions ever settle down). Not sure how those areas are these days.