If you want to shoot snow clad mountains, you can fly to Leh in the winter and move around a bit from there. It isn't accessible by road in winter.
If you want to go to the lower hills, you can visit anytime of the year. Though it is better to avoid the monsoons.
If you want to travel by road in the mountains then the late June to September months are best. The hills are best after September, once the rains recede!
Thanks for the handy info, mate!