On this site, that is the Southeast AZ association of Realtors site, you can perform searches and, by clicking on the home that meets your criteria, you will see all the home features on the bottom of the page, to include heating and cooling.
You can't assume that homes in Prescott have A/C or even in the valley.. We see older homes with evaporation or window units and Bank owned properties with the AZ unit missing.
If you wish to send me one or two that you have looked I will check it out for you.
My guess is they will have AC at this price. Keep in mind the listing may say "Heat Pump: which provides bot refrigeration and heat.
The listing from the Realtors MLS will have more information.
Arizona Homes and Land
If you need assistance in purchasing a property or just want to see what is out there then go to http://www.RanchoElDoradoRealEstate.com and see all that we have to offer.
Maybe another agent in Sierra Vista knows if this is an issue with our MLS?
My suggestion to you is if you find some homes that interest you, click on the link to the office's website to get more information on that particular property.