Is it profitable? Depends on how you define "profitable"!
I bought my last pony for $1200. He only wore shoes in the front. No extra vet bills. I had him for exactly a year and I sold him for $10,000. When you add board, equipment, SHOWS, etc etc I made about $3000 profit. When you do the math, I made barely minimum wage. I was lucky on that one. There are some I've just broken even.
I can tell you right now that board is the biggest killer when it comes to profit. You might be thinking "i'll put 120 days on it", but what if it takes longer then that to get him marketable? what if the market is bad? what if he gets injured? It's hard to sell a horse as soon as he's ready. That $400 adds up unbelievably fast. If you end up having him a year board alone will be almost $5,000. Doing it on your own acreage is much much easier.
I don't know about a lot of other disciplines, but if you sell to a hunter it's going to need to be pretty quiet, they're going to want something with a lead change -preferably auto- (HUGE price difference between a horse that has one and one that doesn't), moves well, and has show miles. That's really hard to make in just 90-120 days. And "prospects" (meaning no show miles, maybe a little green in some areas) are not selling for much these days. If you sell to a jumper it's going to need to be scopy, brave, responsive, need to know how to comfortably do combinations, preferably have a lead change, and again, have show miles. Hard to do in 90-120 days.
I'm not trying to discourage you in this if you really want to do it. But I'd do it for the experience at this point, not for the money. In fact, be prepared in case you lose some. I've been doing it for about 6 years and while I'm certainly getting my name and reputation out there, I am definitely not getting rich!