I'd say they have emotions of happy, mad and whatnot.
One of my favorite memories was when one of my kids' horses met up with a former pasture mate three years later in another state. The two mares whinnied and nickered and pranced around. They sure appeared to be happy.
On the other end of the emotion spectrum, a good friend had a mare who never "liked" a certain gelding. Friend sold the gelding to a neighbor in the fall, and the next spring the horses were both at a branding. The mare got loose, went to where the gelding was tied and proceeded to kick the heck out of him before the owners broke it up. She darn sure appeared to dislike him, and hold a grudge!
But, when it comes to horses doing their job, just like with us, we may not be happy, happy to have to do a task, but just have to. So, my acknowledgment that horses have emotions doesn't interfere with training or work.