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re: As much water as there is on Mars, it is still extreemly dry.
gbaikie — (archived)

Total mass of atmosphere: ~2.5 x 10^16 kg
Water (H2O) - 210 ppm
http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html

So the total mass of Mars atmosphere is 25,000,000,000,000 tonnes.
Or 25 million million tonnes.
You have 210 part of water per million.
Water is lighter than CO2, but very roughly you could simply times 210 by 25 million tonnes. Therefore there is about 5.2 billion tonnes of water in Mars atmosphere.
Or about 5.2 cubic km of water.

"I wonder if melting the ice would do much more than raise the humidity a few measly percentage points."

There is far less than 1 percent of Mars atmosphere which is water vapor. 210 ppm is .021 %.

But when talk of humidity you talking about how much air is saturated with water vapor- and this is dependent upon the air's temperature.
For example in the hot tropics on Earth, if one has 100% humidity then about 5% of the air [50,000 ppm] is water.
And in the cooler temperate regions with say 70 F and say about 50% humidity it would be somewhere around 1%.

As far as the amount water in Mars ice cap:
"Combined, the north and south polar ice caps are believed to hold the equivalent of two to three million cubic kilometers (0.47-0.72 million cu. miles) of ice, making it roughly 100 times more than the total volume of North America’s Great Lakes, which is 22,684 cu. kms (5,439 miles)."
pure-water-ice-at-mars-north-pole

So as far having enough water in regards to adding to atmosphere, there is no shortage. There is about 1/2 million times more water at Mars poles than what is in it's atmosphere.

If one 200 meter in diameter space rock hit the poles or simply the ground with a high concentration of water [permafrost] it could put in the atmosphere somewhere around 25% of water vapor which is currently in the atmosphere of Mars.

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