You can visit Kasol & Tosh at those tym.. I was there at the same time.. weather will be good.
No.. you can experience snow fall..due to snow fall public transportations will not be available on regular basis. but you can take share taxis.. you have to go via bus/taxi to Barseni..then you have to walk towards Tosh/Kheerganga..I was there during last new year.
I travelled to kasol, this new year's eve. And it was wonderful experience. We stayed in YOLO camps near kheerganga river. First day, rest for sometime and then leave for Tosh if weather allows, else explore nearby area & enjoy new year eve in camps in evening with bonfire & music. Second Day, leave early for Manikaran as it can get too crowdy in afternoon. We walked for around 12km from Manikaran-kasol due to huge traffic jam on the way. And if you have some time left then explore kullu.
Yes as it might get heavy snowfall at that time, due to which you can't trek there. But still it's really a charming place, good for new years eve.