Yawp. Fast factsheet here:
http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.htmlFor starters, the remaining atmosphere on Mars is extraordinarily thin. Go to the top of Mt. Everest. Then go four times higher than that. That's the atmospheric pressure at "sea" level on Mars.
It's apparently relatively easy to determine atmospheric composition from afar, and of the atmosphere remaining on Mars, 210 parts per million is water. I have not done the math myself, but I'm assured the total "depth" of water left is measured in microns.
It's really dry. It's really cold. And we'd pop like a balloon stepping outside.
As for how much water is frozen below? SHRUGGGGGG Anyone could make a career answering that. The biggest confounding factor is that the planet is substantially covered in dust, many meters thick in places. It makes remotely sensing what's underneath a real pain in the ass.
The most solid answer so far appears to be "there is a nontrivial amount of ice below the ground". Think "enough to fill the great lakes".