It is safe to travel these days at north side( vaishno devi) If you're looking for a respite from the heat, you visit during summers, and if you wish to witness nature at its best, you can visit during the monsoon. Though, in general, November to May are the best months to visit North India as the weather is quite pleasant during this time.
Yupp certainly.Feb wud have been even better as the old gufa gets opened.Anyways this is a good time too.The only not so good time is August due to landslides danger.