I know in most movies you'd see the hero kick the horse's stomach with his calves. Did you do this? Is this OK for you?

I can never do this .. I just touch gently since I am afraid it hurts the horsey too much :p

I never really like seeing the horse getting kicked in movies. Horses are sensitive so I always just gently pull the reins in the direction I want to go. My horse is smart so she knows when I went to move so I usually just have to gently pat her neck then she starts moving.

Some horses have less sensitive sides than others. I've ridden lesson ponies who were so dead from beginners whopping them like that you practically had to as well. But for most intents and purposes you shouldn't be kicking your horse, you should be squeezing as if it were a tube of toothpaste.

I'm not sure what you mean about squeezing the horses like a toothpaste. What part do you squeeze and how?

Movies are movies and actors might not know anything about what they are portraying so they just do what is written for them to do.

If you kick a sensitive horse you would find yourself on the ground and fast. When you ride you squeeze as pumpkin said. You use your thighs and calves to put pressure on the horses sides and your leg should always be in contact with the horse's sides. Kicking would require removing and reapplying your leg. Have a friend/instructor push on your leg around the horse at a halt and you'll see what it should feel like.