Winter in Sikkim starts from October till march. Thangu, Zero Point, Yumthang Valley, Gurudongmar Lake in North Sikkim are blanked with snow in winters. Gnathang, Old Baba Mandir, Kupup, Memencha Lake, Lachen Village and Chopta valley are some of other place which get snowfall every year in the winter season.
I went to Sikkim in March end and got lucky and even witnessed a snowfall. If u want to see snow the best time would be either October November or Feb end till match end. I had 8 days in hand and I visited Gangtok..natula pass..lachen..lachung..as well as Pelling. I witnessed snowfall at natula pass and tsomgo lake. also a lil snow fall at gurudongmar lake. If u want to explore all of Sikkim..u would need atleast 10 days in hand. however if u want to see bits and pieces of the place 5 days can b okay too.