I have had a horse choke. Not fun and VERY dangerous. Can be fatal. I also know of at least one other (I think 2) horse(s) that have choked. None were caused by apples, carrots, etc.
In my own case, the horse ate too quickly. It was beet pulp that had been well soaked, but he just gobbled it down. Funny because he had been eating this stuff for over a year w/o a hitch. Anyway, I called the vet and in the meantime massaged his feeding passage very firmly to encourage the food to loosen up. I was very lucky -- by the time the vet got here, my guy was 100%. The fix here was #1 the horse didn't need the beet pulp in the first place; it was a carryover from his previous owner and I was weaning him off and #2 put large stones (or like I did, a whole salt block) in the feed dish to force the horse to slow down.
In my friend's case, the horse had not been properly swallowing the food over a course of a few days. So every meal time, a tiny bit more would jam up, but most of it would go down. Finally, it was too much and she choked. This time, the vet had to tube her to get her cleaned out, but she came out fine. Her diet was changed.
The texture of the food won't matter (beet pulp not soaked enough will cause severe problems in the digestive system, but not choke). Usually the cause is eating too fast.