Whoa - that's a really nice trip with interesting options.
There are direct flights but no direct trains for this journey. New Delhi (Delhi) to Srinagar (Jammu And Kashmir) distance is 831 km and you can get there by flight in just over 1 hour and 15 minutes or by train + flight fares starting from ₹ 1690.
It's pleasant weather in daytimes, but can get really cold at nights.