I wonder what the evolutionary purpose of a beard is, 
Most likely to keep the face warm, but i like having a beard because people don't mess with me when i have one.  A beard makes me look threatening.  That may also have some evolutionary purpose.
Yes it seem that it is trait that was left  from the time when humans had hair in their face and entire body.  
Interesting.  i know that when the ice age ended about 13,000 years ago, man had been living in a cold climate.  I wonder if previously to the ice age if man had hair on his body or if it was an adaptation to the cold environment.
It seem to be just the opposite. Of course the evolutionary loss of hair have been more pronounced in certain population like Native Americans and some Asian populations
That is strange.  If we were hairier before the ice age, that would suggest that we have de-evolved.  Am i drawing a correct conclusion here?
Maybe, why do you think having less hair is less evolved I said that evolution have let us to have less hair.
Snow bunnies are white because they live in a white environment.  They have evolved to be that way.  Your thesis is that we evolved to have less hair, even though there was an ice age, and in fact we are currently still in an ice age.  Logic suggests that if we evolved, if anything, we would have more hair during a period of cold temperatures, not less.