The chance of anyone spotting Liz indescribably small... there are over 5 million people in the
general Phoenix area (last time I checked) and a quarter million of that is in Scottsdale. There's a shitload of small horse properties in North Scottsdale. That *used* to be well outside of town, but the town has grown around it and jumped past that area. Shea Blvd is about about half-way up Scottsdale, and the ranches are roughly between there and Bell Road. I camped up there one time when I was a kid 'cos it wasn't anything but desert and lizards. Hell, there's probably a playground there, now.
Big metro areas: no worries about your privacy. If you're in a small town, then kindly don't mention your area of the world. I know a gal that lives in a podunk town in West Texas. She'd spouted off that there were only two bars there. A guy from Dallas stalked her, went to both bars and found her (she'd posted a face pic so it was dead easy). She utterly FREAKED, and rightly so.