Why do dogs love playing in the snow?

Small kids do too, if they are properly clothed.
But from my limited experience, the playfulness is an immediate
reaction to the changed environment, either when it first snows, or
when coming out of a building.
It may be a factor in dogs natural playing with each other, either as
a part of their joint playing, or only appearing as such to observers.

I thought of this question today as I watched my three dogs frolicking
in the snow. I don't know how a real answer can be found, since we
can't know what dogs are thinking, but I suspect that the main
attraction is just the novelty of the snow: it is something new and
different.

In areas where snow is on the ground most of the time, dogs probably
view snow as the norm, and aren't very amused by it. However, if grass
were to fall from the sky, those snow-dwelling dogs would be mighty
excited. ;-)

Pinkfreud, let me just register a note of disagreement about dogs who
live where there's snow on the ground most of the time.  I lived for
eight years in the Sierra Nevada mountains, where there was snow on
the ground roughly nine months out of the year.  During that time, I
had dogs of my own, and I routinely rescued dogs from the local
shelter and trained and re-homed them.  Probably 30 dogs passed
through my hands in those eight years.  And I can say with absolute
confidence that, with very few exceptions, dogs who live in snow
country LOVE SNOW.  Grass?  Bleagh.  Boring.  But fresh snow -- even
during months when fresh snow fell EVERY DAY, by the foot -- fresh
snow was EXHILARATING.
I think they like the feel of it and the taste of it, but even more, I
think snow traps scent next to the ground.  So it's a feast of scent
for dogs.

That's neat to know, Hagan! I stand corrected.

This is a pretty cool article about dogs and snow:
http://www.petpeoplesplace.com/resources/columns/steve-dale/2005-12-15.htm