A low snow winter is but one factor. If we have late snow and very cold spring, you just might need ice axe, crampons and basic snow skills to climb the chute to Trail Crest and, more importantly, get back to Trail Camp.
I've crossed Cottonwood Pass after two big winters in mid-June, once there was about 200 yards of solid ice requiring the use of ice axe and crampons for safety; the other year 20' or so of slush which could be avoided.
Also, in late May 2007 after a mild winter and a warm spring, the the trail was still blocked at the cables, requiring a climb.
All information you get is at this point is a wild ass guess.