Why is not snow melting in Ladakh at a rapid pace
The albedo of the snow would be the primary reason the snow is not melting.  Using a simplified model there are two main sources of heat energy that the snow can absorb, the heat from the ground below, and the heat from the sun and atmosphere above.  The ground and the atmosphere are going to be colder at high elevation because of the lapse rate that gansub mentioned in his comment, which effectively leaves radiant heat from the sun to warm the snow.  Snow is a good reflector of near infrared to UV, the linked document on the top of page 206 shows the albedo for wavelengths from 400nm (blue/UV) to 900nm (near IR).  On the table you will find that the minimum albedo for snow (assuming fresh snow) is above 0.8 or 80% or better is reflected. 

One aspect that might be confusing is that I don't believe you are getting a sunstroke, a body heat issue, but instead a sunburn.  Sunburns are damage to the skin from UV radiation.  At high elevations the UV from the sun is not filtered as much as it is at lower elevations, in addition what does make it through gets reflected back by the snow, effectively doubling the UV exposure when you are in a snow field.  See this site from the World Health Organization,