Socorro is a small town (population about 8,000), so don't expect a really top-flight Kosher Vegetarian Chinese place (like the one in Cambridge) or the usual amenities of huge cities. However, if you are a vegetarian, you won't have to starve here, even if you prefer not to cook.
I lived in California long enough to be aware that ``vegetarian'' means vastly different things to different people. There's sort of a Richter scale of people that use the V word---from strict vegans, to people who will eat dairy and eggs, or fish, or chicken, or even pork! I know it sounds silly, but there are people who call themselves vegetarians but will in fact eat anything but beef. Obviously the pure vegans will have a narrower range of options.
Back when Martha's Black Dog was open, vegetarians and even vegans had one good option. Now, I'm afraid it's mighty thin.
If you like Chinese food, the Hong Kong (on the main drag at Otero, adjacent to the Economy Inn) has numerous vegetable dishes. It's good honest Mandarin food. Warning: may close or move in October 2005.
There's a 24-hour coffeshop (El Camino Restaurant, on the west side of the main drag around the middle of town) that has some vegetarian selections. Not too bad, nothing fancy, honest coffee shop food. We have a Denny's that isn't too much worse than the norm for that chain.
The Mexican restaurants tend to put meat or meat stock in almost everything, but ask the waiter and there may be some options.
If all else fails, there's always home cooking!