No, from what you have written it does not sound like you are cruel to the horse.
However, you should take a moment to evaluate how you interact with him. Does he need these corrections a lot? If so, can you establish why and try to fix the problem or do you just smack him/correct him?
Also, especially for non-horsey people, your attitude comes into play with why people might say you are cruel. If you calmly give the horse a correction and proceed along with your day that is one thing. It's entirely another to get ****ed off, over correct the behavior, and then continue with tight reins or hard hands for the rest of the ride all while cussing and/or yelling at the horse. I will freely admit to loosing my cool with Rio twice and I am very glad that no one was around to see it happen either time. Even though I inflicted no physical pain on him (I don't use whips, spurs, etc) it was not behavior that I am proud of and he didn't deserve my attitude. In reality by me blowing things out of proportion I probably set back our progress but in the heat of the moment I was seeing red and it took me a few minutes to realize I needed to be done for the day.