There are lots of places where you can shoot a public-lands mule deer in the west fairly easily if you are willing to work at it a bit and use the right tactics. Many western states have "draws" for tags nowadays, and the best areas often have poor odds of drawing a permit. You should do a bit of research on which states offer the best opportunity.
You can hunt mule deer under a variety of conditions, as well. They range from the wide-open desert landscapes of the southwest to the classic high-altitude hunting found in the upper reaches of the western mountain ranges. You can hunt them in sweltering conditions, or in sub-zero temps. Again, if you are looking for a particular type of experience, do your research.