These are the conditions when we climbed Whitney on the 2-3rd June.
The trail from the Portal to Trail camp is almost completely clear of snow with only a few patches of any size which should not cause problems in either walking or staying on the path.
We started from trail camp around 8am and although the snow was a little hard I did not use or need the crampons I was carrying but did use my ice axe in the lower area around where the cables are normally run. I did not need it to cut steps. On that day this was by far the most difficult section although not that bad with the right boots on, it was also slightly tricky higher up. I could have got away with just ski sticks as others did. (Tip-shorten the up hill stick and remove the basket to use as a dagger, plus learn to break with a ski pole). What people were struggling with big time, were boots that were not stiff enough to kick a step into the snow or hold an edge. Trainers are a definite liability at the moment! After trail crest the path is generally clear except for the odd patch and the snow field near the top which is not steep.
We were descending around 4 pm and the snow was still soft. I did don my crampons but only to do the big slide to the left of the switchbacks (looking down). If you do this stay well to the right of the slope (looking down) to avoid the rocks. The snow was quite rough and although it only took 10 mins to descend it is probably best avoided.
If it had been freezing hard (which it was not at 4pm) crampons may have been needed on the switchbacks descending so be wary if you are descending late or on a cold day as this slope goes into the shade quite early making retreat difficult.
In my view and it has been stated here already Whitney is not the place to put on crampons or use an ice axe for the first time, it is easy to trip yourself up, and/or stick one of the points in your own or your mates leg, also they can cause you to cart-wheel if they catch should you slide down some steep snow.
The lesson should come before the test!
To sum up on the day we did it no axes or crampons were necessary, but stiff boots and sticks were, however if you plan to descend late or its cold then they could well be.
Hope this is of use.
Have fun.