No, not all snow tires are studded.
When I was about 20 and living at 9,000 ft in Colorado I spent an entire winter driving a rear wheel drive SUV with only 2wd and just run of the mill all terrain tires. It sucked but miraculously I never actually got stuck. It can be done but.... Is a 4wd vehicle with decent clearance not an option for you?
I remember years ago being the last guy to leave a job site after some heavy snowfall during the work day. Long day of work, sun going down, strong wind and coooold. 2wd F150 with good tires that got around pretty good. Not that day of course. As I shoveled the drifts away I vowed to buy a 4wd vehicle and never look back. Point being, it worked great until it didn't, and then it sucked at the worst possible time.