For your first hunt, I would seriously recommend this guy and hunt Wyoming.
http://www.headinwest.net/ The learning curve is tremendous and it is money well spent. Most of the time, new hunters spend 5 years + before being successful .
Someone mentioned, " just go,don't over think it ". That is fine if you want to go on a camping trip and hike around with a rifle. 10% of the hunters, kill 90% of the elk, they don't do that with that kind of attitude.
This is some of the best advice in the thread. I began elk hunting exactly the way the OP is suggesting, minus the horses, and would have been much better served by going with an outfitter. In addition to the cost of gearing up being fairly close to that of a guided cow hunt (as George accurately pointed out), I didn't have the time to scout elk, nor did I really know how to find them with any real skill or consistency. I hunted CO first rifle season, which is only five days. It's not easy for a brand new elk hunter to roll into an unfamiliar area, find elk and punch a tag in five days. I look at a guide the same way I would view an education. Pay your tuition and enjoy the benefits for the remainder of your life.
As a side note, the shot opportunities out west usually come and go much faster than the typical deer hunting we are used to in the Midwest. We get spoiled out here, waiting for deer to turn at just the right angle for our preferred shots. Do that out in the mountains and you'll likely be waiting a very, very long time. Be ready to take a quick shot the moment you get a good opportunity.
