In Colorado, landowners have the inherent right to fence their land or leave it unfenced. In the early 1880's the Colorado legislature passed a "fencing" statute. This statute is commonly referred to as the "open range" or "fence out" statute. "Open range" is a definition of land, not a law.
“Livestock” includes horses, cattle, mules, asses, goats, sheep, swine, buffalo and cattalo. The Colorado Revised Statues 35-46-102 states in part “If no fence exists, animal owner not responsible for nonwillful trespass. One who turns his cattle out to graze, unrestrained upon lands where he has a right to so release them, is under no obligation to prevent them entering upon the unenclosed premises of another.”
Most livestock owners do not intend for their livestock to stray and will respond quickly to recover them. Be aware of who is running livestock in your neighborhood. If you find livestock running loose, try to notify the owner immediately. If you do not know who owns the livestock, contact the local brand inspector and the sheriff's office. If the livestock are in danger and loose on a public road, try to contain the livestock and move them away from the road. Call for help immediately from neighbors, the sheriff's office and the local brand office or inspector. Any thing you can do to avoid an accident will be greatly appreciated by the livestock owner and the general public traveling on the road.
The necessity to have a fence to protect your property in rural areas is no different than in urban areas. In urban areas you need to have a fence if you do not want unwanted guests on your property. The same rule is applicable in rural or country settings. The difference is the critters trespassing and the volume of space requiring a fence. Protecting yourself is the main idea.