My friend organizes a running event every year, Manali to Leh running in which runner has to run 480km in 120 hrs. So I volunteer at this event every year. The runner has to reach Leh from Manali in 5 days. That's why we have a lot of time.
It is really very crowded in June, the rates of everything from hotels to water become high.
If you like winter then come to Leh once in winter. The feeling of temperature of -20 to -30 degrees is different. Once I did Chadar trek there in Zanskar valley, this trek is on a frozen river.