I summitted Whitney by the Mountaineer's route yesterday.
The snow in the chute has not been refreezing at night lately, hence there is 6-18 inches of soft snow over a harder base. This is true almost everywhere, except near large exposed rocks, where it can form bullet-proof ice and is making some moats. This was especially true in the final gully to the summit.
I carried an ice ax and crampons, which I was glad to have. I was still wary of the highest-angled section of the lower chute. On the way up, I avoided it by traversing climber's right to class 3 or 4 rock. On the way down I avoided the steep section and a mountain of loose rock beside the snow by moving descender's right of a large tower onto a ramp of reddish rock that later turned into a gully and some blocky, but generally unexposed class 4.
After reaching the notch, I took the first gully to climber's left. It required a rather bouldery, scary move to get from the snow onto the rock because there's a bit of a moat, and the rock in the gully is wet from snow melt. The final gully was straightforward class 3 until the last half, where currently there's a choice between difficult-looking, exposed climbing on either side of the chute or a steep snow slope (perhaps 50 degrees?). I took the snow slope. It was fine on the way up, but scary on the descent because of the exposure. Luckily the snow was again quite soft, but I wasn't about to find out how far I'd slide on it.
It would be a whole different route if temperatures got below freezing for a while. I would be reluctant to climb it in those conditions without a belay, given the amount of snow on the route still.
Pictures:

The route I took as best I recall. Ascent in red, descent in blue.
<img src='http://pages.pomona.edu/~anm02002/whitneyMR/images/mr0041.jpeg.jpg' border='0' width=800>
About halfway up the chute.
<img src='http://pages.pomona.edu/~anm02002/whitneyMR/images/mr0046.jpeg.jpg' border='0' width=800>
<img src='http://pages.pomona.edu/~anm02002/whitneyMR/images/mr0048.jpeg.jpg' border='0' width=800>
<img src='http://pages.pomona.edu/~anm02002/whitneyMR/images/mr0049.jpeg.jpg' border='0' width=800>
Views of the final gully to the summit. Note the ice near the rocks in the first picture.