Are you referring to the hole in the hoof wall, on the right side? No, that's not an abscess, it's just a part that's missing. I would bet it developed because of lack of hoof care, though. Like others have said, he needs a farrier to work on his feet like yesterday.
As others have said, can't see anything in that unclear pic that says 'abscess' and if he's not lame, I wonder what would make you suspect it anyway?
As others have said, he is long overdue for some good hoof care. For your info - & your horse's benefit, you need to know that it's important to get a farrier to attend to their feet regularly & 4-8 weeks is the average schedule that horses need trimming. I advise you learn more about hoofcare & management. Also diet is hugely important for health & ponies especially may need to be managed carefully in this regard & not left on good pasture. Horses also generally need a dentist approximately yearly to 'float' their teeth, as they keep growing & can become sharp & imbalanced. If you need any other info on care & management of horses, just ask. There are no such thing as stupid questions, it's only the ones that are unasked & lead to neglect through ignorance that fit that bill I reckon.
No feet...no horse. It is that serious. There are some things you can neglect about a horse and not see consequences for a very long time. Feet do not fall under that category. I'm surprised that you got away with it this long. His feet are in horrible condition, IMO, and badly in need of a farrier. We can't help you fix this. You need a professional to start working on those hooves.
If you can't afford a farrier, then give him away or shoot him. I don't want to sound mean, but his feet will continue to grow and the problem will only get worse. If you keep him and are unwilling to provide the care he needs, things will only get way worse for him. Why let it get to the point that he is in so much pain he can't walk? Get him a farrier, or get rid of him. He doesn't deserve to suffer.
Not just soon, he needed to see a competent farrier long before his feet looked like that.
I get the impression that you are quite young, and it may be up to your parents to make the call (and I'm very very sorry if that's not the case ), but understand that a scenario like this is extremely frustrating to those of us reading it - there is no excuse for his feet to be that bad, period. Going by this thread and the other one you put up about this pony, I'm very concerned that he may founder. By putting off making the phonecalls and getting someone out, you're playing with fire.