In the state of Georgia, you can get a license with an associates degree or with a bachelors degree. It may vary by state.
What you get to do is to set up equipment for surgery, process x-rays, take x-rays, do wound care, give injections, bandage wounds, pull blood, and a whole lot of other fun stuff. Everything that you do will have to be under the order of a veterinarian.
You may not legally diagnose illness, prescribe drugs, or perform surgery no matter how minor.
You will also get kicked, bitten, stomped, and otherwise abused..........
If you want to get a job working with horses, you need to be willing to move to a good job. You can't just stay in your home town unless you are lucky.