The atmosphere of Mars would count as a vacuum on Earth. There is no way you could survive without a spacesuit, just like the Moon. Yes the atmosphere is thicker at the lowest points. Still, the maximum boiling point of water on Mars is 10C, to take an example.
The highest pressure is 12.4 millibars at the bottom of the Hellas basin (also the location with the 10C boiling point for water). That is a little over a hundredth of sea level atmospheric pressure on Earth.
By comparision the atmospheric pressure in the “killing zone” at the top of Everest is a third of Earth atmosphere. Some extremophiles on the Earth can survive a vacuum, and would be able to reproduce on Mars in e.g. thin films of salty brine which may exist on the surface, or the evening and morning “dew” that may briefly form on the rocks.
Nice answer, but I have to point out that you have responded to a thread that has been inactive since 2004, many participants are probably no longer here, and many of the responses will be some (no longer funny) variety of zombie joke - the usual reaction to the resurrection of a long-inactive thread.
i.e. How much atmospheric pressure do zombies need to function?
Anyhow, since the thread has resurrected and there is a remake of Total Recall soon to be released…
One of the early sci-fi books I read was James Blish’s Welcome to Mars - the protagonist breadboarded an antigravity machine and went to Mars in a packing crate with a minimal supply of food and oxygen. Unfortunately, the vacuum tube powering the antigravity system failed (damn tubes) and he was stranded. In 1968 it was thought that the partial pressure would be almost enough if you headed for a low-lying region (like the Hellas basin), so that is what he did. Of course, later probes showed that this would not be possible, and our protagonist would have died. Good fun though.
However, the book was part of the kick that pushed me into scifi reading, along with Heinlein and Norton - stories like Have Spacesuit, Will Travel and Dark Piper.
Si
In KSR’s RGB Mars trilogy, eventually the characters do survive outside with only bottled air but that was only after the atmosphere had been thickened substantially, though it was still unbreathable. As noted up-thread, Mars, with only 1% of Earth’s air pressure, it is for all practical purposes, a vacuum.
We can assume that zombies no longer need oxygen to function, so the basic lack of ambient oxygen wouldn’t present a problem. They also won’t be bothered as much by rupturing capillaries or gas pockets swelling under the skin, although that may depend on which type of zombie you’re talking about. Ultimately, dessication of the tissues as the water and other fluids boil away will probably result in the zombie falling apart or otherwise becoming immobile, although again this will depend on what kind of zombie it is. A Rage virus type zombie will ‘die’ quickly, while one animated by necromantic magic might remain walking even after being reduced to a skeleton wearing scraps of freeze-died flesh.