There is a great window just after the monsoons are over and before the extreme cold of winter sets in - mid-October to November-end. The best part about this window is that you can get to attend the Darjeeling Carnival, which generally happens in the second week of November. Moreover, the weather is absolutely smashing with pristine blue skies with little worry about rain or snow.
Hi Mitali, For Sanakphu trek, The first season, with the temperature ranges from 8 to 15 degrees, is from April to May and the second season is after the monsoon starting from October to early December when the temperature ranges from -5 to 5 degrees. For Sikkim- As suggested by Sikkim Tourism, the best time to visit Sikkim is either between March and May or October and mid-December.