'Horse' from 'America's Got Talent' -- CHEATS DEATH ... After Tree-Smashing Car Crash

"America's Got Talent" star Zac Gordon ... aka Horse ... aka the guy with iron testicles ... is lucky to be alive ... after smashing his car into a tree while trying to avoid striking a deer, TMZ has learned.

Horse -- who became famous for allowing people to bash him in the scrotal-region on AGT -- tells us he was driving in Harrisburg, PA Saturday when a deer suddenly ran out in front of his car. Horse says he jerked the wheel, trying not to kill the animal ... but lost control and went careening into a tree.

Zac says he hit the tree so hard the car flipped over -- "I legitimately thought I was going to die."

An ambulance rushed to the scene and hauled the AGT star off to the hospital. He was released later that night with a possible concussion, sore neck and scratches ... but luckily no major injuries.

"I'm just glad to be alive," Horse tell us.

Now, here's Zac crashing into other things: