Ask Mr. Smarty Plants

Quickly, before we cover the rest of your question - no, it is never all right to dig up plants in any area, open or not, without permission from the landowner. We are familiar with the area you are talking about, and some of it is national forest, some state parks or historical monuments, but all of it is owned by someone, either a political entity or a person or a corporation, or a Native American area. What looks like plants all alone out in a desolate area could even be threatened or endangered plants, being allowed to propagate themselves in place, in hopes of increasing the population of that plant. And, in most areas, rural or urban, it is a felony to remove anything, even plants, from a property without express permission.

Now, to try and address your specific question. There are 18 members of the genus artemisia native to North America, 10 of those native to Colorado and 9 to New Mexico, and all having the word "sagebrush" as one of their common names. Our choice as the best possibility is Artemisia tridentata (big sagebrush), which is native to the area around Taos County, in north central New Mexico (USDA Plant Profile) as well as to Adams and Jefferson Counties in Colorado (USDA Plant Profile). 

What should be noted is from our Native Plant Database page on this plant:

"Plants are extremely drought tolerant and are susceptible to root rot if too wet. Nitrogen-fixing.  Commercial seed of this species may belong to one of three common subspecies: Basin - tridentata, Mountain - vaseyana & Wyoming - wyomingensis. These subspecies are adapted to distinct environments, so it is important to identify seed sources."

The point here is you could dig up (please don't!) or purchase a plant or even seeds labelled as Artemesia tridentata and move it from New Mexico to Colorado,  but it could be a sub-species adapted to a different environment. This article from Plants for a Future Artemisia Tridentata indicates that it is propagated by seed. Seed production is from October to December; seeds germinate as early as April. Therefore, if you purchase seed, you should be ready to plant it no later than December.

Since we are in doubt that plants or seeds purchased from a nursery in New Mexico would thrive in Colorado, we suggest you contact the Colorado Native Plant Society for some information. That Society also has a Links page which will help you narrow down the area you are studying. For even closer to home information, contact the Colorado State University Extension Office for Adams County or Jefferson County. Finally, go to our National Suppliers' Directory, type your town and state in the "Enter Search Location" box, and you will get a list of native plant seed suppliers, nurseries and consultants in your general area. You can contact them for seed purchase, and remember to ask where the seed was collected.

Pictures of Artemisia tridentata (big sagebrush) from Google.