Conditions on Williamson were generally good. The trail up shepherd pass still has a patch or two of snow, but there's an easy-to-follow use trail around it. Traversing the Williamson bowl was not as bad as I was lead to believe online. There were a couple sections of serious talus (big and loose), but mostly it was pretty easy cross country travel. We walked over a few sections of snow, again quite easy, no spikes needed. Above the black stain, we found a couple patches of snow that could easily be by-passed by sticking to one side. The chimney was in good conditions, as was the scramble to the top.
Unfortunately, our weather window closed on Sunday afternoon, so we couldn't climb Tyndall, but the North Rib looked good to me.
I posted some pictures that I took on Facebook (should be publicly viewable):
https://www.facebook.com/xiainx/media_s ... nref=storyNote that this was all 2 weeks ago, and since then there have been several storms in the Sierra, so this may have changed. For example, about one week later I was up on Whitney, and the Whitney trail was all covered in snow and ice. Fine on the trail, but I went to try Mt Muir and bailed because I couldn't get any solid hand/foot placements.
HTH! Let me know if you have more specific questions