Just be sensible. Check shoes before you put them on. Do not overturn rocks or other debris with your hands. In our 2 weeks we only saw one snake (in the wild) - not sure what it was, and were lucky enough to see a large fat Gila Monster (lucky to be on top of a horse at the time). It seems there is no antidote to the bite of one of these lizards though they are rarely fatal to a healthy human however you are likely to suffer excrutiating pain!
When visiting southeastern Arizona one must be sure to have water available when traveling. If you are going off the beaten path you should let someone know where you are heading.
Also, you should be aware of the wildlife in this part of the country. There are rattlers, scorpions, tarantulas, gila monsters and cougars. The chance of an encounter is slight, but visitors should be alert.