I was up there this weekend. The vast majority of the climbers are going up the Winter Lion Head trail. There are boot ladders up the headwall, right gully, right right gully, and all the usual suspects. I went up in my tele boots without a problem, no need for crampons. In the early morning or if the weather gets colder, it'll be froze up and crampons/axe might be needed. Climbing down the headwall wouldn't be prudent right now, Lion Head or Boott Spur would be much safer.
There was snowcover on the trail down to Pinkham, but it was slushy in the sun and there are some bare patches.
What conditions specifically are you looking for?
-dave-