You'll have no trouble with a string of horses in that area. Or longhorns, or bison, or cattle or....I took riding lessons with a woman up in the Elizabeth-Larkspur area and she had a half dozen of them, and 40 acres of land to roam on. I see many large horse properties up that way. Whole area is rural. The further east you go, the more rural it gets.
Parker may be a different story as its built up and there may be restrictions. A realtor would know of restrictions.
Parker has the Colorado Horse Park, where they have many events. See:
http://www.coloradohorsepark.com/
The main E-W road thru Elizabeth is CO-86. Its a small town, in the center of town, just off the main drag, is a BBQ joint. Bennett's? Been there, food is great and plentiful, people are friendly too.
The whole area, staying east of I-25, from Larkspur up thru Elizabeth, up thru Castle Rock and on up into Parker is critter country. The further east of I-25 you go, the better. The whole area is worth looking at.
Douglas County Fairgrounds, Castle Rock, is a major horse venue, great facilities.
http://www.douglas.co.us/eventscenter/
s/Mike