As your horse ages, the teeth get more and more worn down. This can cause senstivity to things like hot and cold, and to all types of sugar. I actually have this issue. I don’t have a lot of enamel on my teeth, and it causes me to be senstive to certain things. Carrots don’t have a whole lot of natural sugars. So my best quess would be that.
Also, did he have a bad experience with something apple flavored? Horses don’t forget things. It can even be a bad spook or other traumatic experience and then you fed him an apple. It’s called negative association. Horses are very strange thinkers! 🙂
If he starts doing weird things with his food or goes off other things he will normally eat, please have an equine dentist out, not a vet. The dentist is specialized, and they are so much more thorough.