You'll probably be fine on the Osceolas as far as snow. Mt Washington observatory is reporting consolidated snow and ice starts above 4,300 feet. I'm beginning to carry some instep crampons or stabilicers along with winter clothing. Higher summits tomorrow are only supposed to be in the 20's. Minimal water crossing on Osceola also. Hancocks are a bit trickier, more remote with more water crossings. Not sure if they'll be any snow at all but I'd be prepared.
MWO quote "by 4300 feet we encountered full on winter conditions."