My sim was level 9 riding skill when she first adopted a wild horse. Waiting for the horse to come around so you can interact with it to build a relationship takes a while .. they come at odd times, often at night, and you sim may be too busy at the moment... so here's how I did it.
0) Before you start, make sure you have the "Wild animals friendly" sign on your lot (its in Buy Mode, under outdoor I think) this will encourage wild animals (racoons, deer, horses, etc) to enter your lot.
1) when the horse I wanted wandered onto my lot, I went into build mode and built a fence around it. I provided food and water, a gate that locks against pets, and whenever my sim had time she would interact with the wild horse a bit.
2) Once the horse likes your sim well enough, you'll have the interact option "Adopt wild horse". You may have to try this interaction a few times, it appears that sometimes it ****** the horse? But it does work.
3)once you've successfully applied the "adopt wild horse" interaction a window will pop up that says "(sim name) would like to adopt a wild horse. Is this ok?" select "yes" and another window will pop up giving you the option to name the horse (you wont know the gender of the horse at this time, but don't worry, you can change the name at at any time later under the "care" interaction of the horse).
4) Tada, you're done, you've adopted a wild horse. The horse will still be untrained, so make sure that your relationship with the horse is high before you start riding him .. otherwise your relationship will quickly drop and you'll eventually lose him as a 'friend'. When You DO start riding him, focus on types of riding he'd enjoy (if he's fast, race. If he's agile, jump. etc) and he'll become trained much more quickly.