Because Smokestack Rock is on private property, it is very important to seek permission first before any attempts. The landowners live just to the north of the summit at the base of the rock. It is best if you inquire there.
Getting There & Route
It is only a short, but steep bushwhack to the summit from the home of the owners. The lack of heavy forestation makes this a line of sight venture. If the owners will allow it, a more scenic route is to hike along the south side of Smokestack Rock into Coyote Canyon, then ascend the gentler slope on the west end and follow the game trail on the top of the ridge back to the east to the rock composite column that is called Smokestack Rock.
Climbing the rock column is highly inadvisable, since it is a rock composite and crumbles a little too easily. The probabilities of a climbing accident would be high.
Red TapeThis is on private property, so "red tape" is whatever agreement you have with the landowner.
When to ClimbWeather will probably be the greatest factor to influence your choice of when to climb. Factors like summer lightning, 100-degree weather or winter blizzards make postponing such a climb to a better time a good idea. You can access the weather for the area at this link:
Smokestack Rock - Scottsbluff Area Weather
Camping and Lodging Resources
Scottsbluff-Gering Chamber of Commerce
Bridgeport Chamber of Commerce