At the Straight Dope website I found a similar question to yours.
Why is there snow on mountains in the summer?
The reason that there is snow on mountains in the summer is that it
hasn't melted yet. Several factors go into the speed with which the
snow will melt.
The temperature decreases with altitude:
As you go higher, the temperature decreases. This is due to the fact
that the earth stores heat from the sun, and the higher you go, the
less earth there is around you. Obviously, the colder it is, the more
time it will take for the snow to melt.
The next factor is the sun: it has a bit of a warming effect, so even
if the outside temperature is 32 degrees Fahrenheit, the surface snow
will want to melt because the sun is beating down on it.
The next factor is the volume of snow: the more there is, the longer
it will take to melt, because the snow underneath the surface will
have a cooling effect on the surface which is counteracting the
warming effect of the sun and air. This is easily demonstrable in your
own backyard: put a one-pound block of ice next to an ice-cube on your
patio on a warm summer day and see which melts first.
Source: Straight Dope Website
Why Does Temperature Decrease With Altitude?
Air is thinner at higher elevations. There are fewer heat-absorbing
gases to absorb and reradiate earths heat
Increase in altitude results in a decrease of air pressure, molecules
that were once packed tightly together have now spread out and are
less dense. Earth is reradiating heat in long-waves, which are not as
hot as the incoming short-waves
The lowest elevation at which snow remains on a mountain during the
summer is called the snowline. A mountain that has no snow in the
summer has no snowline. The snowline moves up and down a mountain
seasonally - lowest in late winter and highest in late summer.
The snowline is related to air temperature, which in turn is
influenced by elevation and distance from the Equator: air temperature
drops as elevation increases and distance from the Equator increases.
Even in areas near the Equator, there are some mountains that have
snow year-round at their highest elevations, whereas in Polar Regions
permanent snow can be found close to sea level during the summer
The snowline is highest - that is, less of the mountain is covered
with snow in the summer - on mountains closest to the Equator. The
snowline is lowest on land closest to the poles. The greater the
distance from the Equator, the less elevation is necessary to
establish a snowline.
The snowline also is influenced by the amount of yearly snow fall.
Thus, the snowline may not be the same for all mountains at the same
Source: U.S. Geological Survey Lesson Plans
Additional information that may interest you:
Temperature Changes and Altitude
why is there snow in the mountains
Altitude and temperature
Thank you for your question and I hope this response has provided you
with the information you were seeking.