I checked the idea some people posted, unfortunately none of them matched up. I did some digged through moby game descriptions from what I thought was the right time period but didn't hit paydirt their either. There were a surprising amount of games though, and I admit I didn't have time to check them all.
I can't think of anything with the little details you gave us, maybe someone else will find out what game it is. Can you remember other things from the game? There's been tons of DOOM clones and sprites-based FPS games over time, but only a very small portion of them have a multi-race/character/faction feature (I.E being able to chose between two or more characters, factions or races before starting the game). And since it was a demo in a magazine then it's possible that the final product didn't make it (just saying it's possible).
I know, its not much...I thought for sure 'Mooman' would find it while I was searching and googling, but that seems to turn up nothing close. It is possible it never made it to release form...however given that it showed up on the PC Gamer demo disk that seems kind of unlikely.
I don't have much else to go with...the graphics were roughly doom to Duke3d quality (hopefully my faded memory has not elevated them) It had multiple platform heights, like doom...so it wasn't like wolf 3d where there's uncolored floors with no vertical movement at all in the game.
One of the weapons (not necessarily the Mooman/Cowman's, I cannot remember any other races right now) was a crossbow...there was possibly some kind of club.
When you picked your class/race it showed a fullscreen picture, probably with stats...since it was a FPS game this is obviously the only reason I know the Mooman existed. He was pretty much just a man body with a cow head. The fact some one brought such a stupid concept to fruition is what interests me most...the game seemed to take itself pretty seriously otherwise. The graphics were not particularly cartoony.
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