The pressure over large areas of Mars are below the triple point, so some kind of flash evaporator or sublimator would work.
Even if it works, it would consume a lot of very precious water.
Also the insolation is much lower, so cool requirements will not be as stringent as on the Moon.
Yes, but a pressure suit has to protect you from both temperature extremes. The usual approach is to insulate you as much as possible, then use active cooling to get rid of the waste heat from astronaut metabolism and PLSS operation. It would be quite a challenge to design a suit that could eliminate waste heat passively while still protecting you from the rather wide temperature swings on Mars.
Also, the fact that Mars has a (thin) atmosphere may interfere with the thermal blankets used as suit insulation. A typical example consists of alternating layers of aluminized Mylar and a Dacron netting. They work in a vacuum much as a Thermos bottle does, with radiation barriers of reflective metals alternating with vacuum gaps to stop convection.
One of the more interesting suit cooling systems I've seen proposed is based on hydride compounds. They usually produce heat when absorbing hydrogen and absorb heat when losing hydrogen, but different alloys do so at different temperatures. The idea is to use one hydride to absorb suit heat at a suitable temperature (e.g., 10C) while absorbing the liberated hydrogen in another material that does so at ambient temperature. You can control the cooling level by regulating the hydrogen flow between them. After the EVA, you heat the second hydride container and cool the first, driving the hydrogen back the other way and regenerating the cooling unit.
I don't know if this has been taken beyond the early prototype stage.
