That can get long and tiring if you aren't flying!
There are direct flights but no direct trains for this journey. New Delhi (Delhi) to Leh (Jammu And Kashmir) driving directions for the distance of 1246 kilometers. It will take at least 21 hours 31 minutes by road and will cost you at least ₹ 6230 of fuel!
Stupid question, but, do you really wanna go someplace that cold ?