You actually don't really need to add dirt to your vermicompost.  You can add a cup or two of regular soil from your back yard to add some beneficial microorganisms and also some grit.  Worms have gizzards (like chickens), so they need some kind of gritty material to help them with digestion.  Finely crushed egg shells are also great for that!

I suggest against using peat moss for anything because it's not a very sustainable resource.  Instead, for bedding you can just add a lot of newspaper, or you can also use a peat moss alternative like coconut fiber/coir, which helps to absorb and retain moisture.

The climate in Albuquerque is certainly different from the Pacific Northwest,  but it's definitely still possible to successfully compost and raise worms here! 

There are a variety of methods to compost, and I myself have several different composting systems set up.  I do a lot of vermicomposting, with worms, and have several bins set up inside.  Since they're inside, temperature isn't an issue, if the temp's ok for you it's ok for the worms.  They're relatively easy to take care of and don't smell; they're especially great this time of year when it's cold outside and I can just compost inside rather than having to take it outside on days like today when it's snowy.

That being said, I also have several systems set up outside as well.  If you're doing an open air heap, the worms will be fine, they just migrate towards the middle of the pile if it gets too hot or too cold.  If it's roughly 3 X 3 X 3 feet, its a big enough size so the interior climate should be fine for them.  If you have a closed system, like a barrel composter, and want to put worms in it, it's a good idea to put it in the shade during the summer months so it doesn't get too hot, and keep an eye on it to make sure it stays moist enough.  

Here in Albuquerque, with the dry climate, moisture can definitely be an issue with composting.  Basically, if you have an outdoor system, it's nearly impossible to over-water it.  Because we live in a dry climate where water is scarce, I also don't like to use fresh drinking water simply to moisten the compost.  I have a big bowl I always put in the kitchen sink to catch water when I'm rinsing vegetables or fruit or washing and rinsing dishes. I empty the bowl of water into a bucket I keep in the kitchen, and then pour the bucket on my compost whenever it gets full.  The water you dump on your compost doesn't have to be clean; if you use biodegradable dish soap, the soapy water is perfectly fine to dump on your compost.

You can also lock moisture into your compost and minimize evaporation by covering it.  Some people put a tarp or other large sheet of plastic on top, others use a section of old carpet or rug.  Dark colors are best since they heat up more.  I prefer to keep it natural and make sure I always have a thick cover of leaves to keep moisture in.  Pull back your tarp, rug, etc, or bury down into the leaves to deposit fresh food scraps or other organic matter to be composted.