If you want to experience winter Ladakh, which i found to be magical, then visit during Dec-Mar. The locals are free during this time, lot of snow around and chances to spot snow leopards as well. But it will be very cold during this time, so one has to be prepared. Follow my blog to get details.
So it’s the month of may from when the Leh vibe boosts up, the riders start their drive from the month of May.
It depends, how you want to travel from your starting point and which route you are planning to take.
You can just drop what you are looking for on the comment box and I can tell you what itinerary you should follow.
May second week to third week as that time it's not so crowded.Moreover you can enjoy the snow capped mountains .I have been there thrice but still want to visit again.