There's some likely water in the initial miles out of Patagonia (beyond the high-grade road walk). Then you can pick from Enzenberg Canyon, Bowman Spring, Scholefield Canyon (a few tenths up the wash for pools), the Lake, Twin Tanks, and Cienega Creek, some of which are almost bound to have a bit of water in early spring except in an unprecedented drought. I don't think we're there yet. In fact, I hear Cienega Creek currently has a deep, yards-long pool with minnows right where the AZT crosses. That should be there to one extent or another into March at least.
Rincon Creek can be a heartbreaker. I wouldn't count on it. Until SNP decides to renovate Hope Camp with a nice solar well, there are at least two canyons the AZT crosses beyond the Quilter Tr junction that often have water in spring. The second one (beyond the junction from Madrona) might be more reliable (big pools in spring 2010). If you see water here, good chance of seeing some at Grass Shack too.
North of GC you can normally melt some snow during thru-hiker season. More problematic could be from the San Francisco Peaks north to GC, though it's not normally a big deal in a season of average moisture, esp. if you're ok with drinking tank water. Snowbowl definitely has water inside the main building, but access could be an issue outside of ski season.