If you are wanting to learn about cows and working cattle with horses, try a feedlot as a pen rider. They are sometimes willing to take someone who is green if that person really wants to learn the business and is willing to work hard.
I recommend that if you don't know cattle, their general health and illnesses and don't have really handy horses yet. Ranching is all about raising beef. We are just fortunate to have horses as fantastic co-workers.
Dude strings offer some horseback hours, but saddling and unsaddling a string of twenty might bother the legs. Outfitting, at least in my area, doesn't offer much horseback time and you're more like the waiter, housekeeper, cook, and chore boy for the hunters than a horseback hand.