"It depends"
I didn't want to be the johnny raincloud, but since you started....
We wanted to breed our mare when we thought we'd have to retire her early. We would have had to have her stall torn out and built a foaling stall (twice as big as a regular stall), fence in separate pastures for mare and weanling, and get rid of our other horse to have room to keep the weanling. The stallions we liked were about two thousand dollars a straw - no live foal guarantee. It's off as she recovered from her injury...but the vet warned us - after not being bred for years while being ridden...we'd have a hard time getting her in foal. A real hard time. Our pastures aren't really big enough and our property isn't really big enough to get the foal completely weaned, and we would have had to replace ALL our fencing with foal/weanling/yearling safe fencing.
You're younger and healthier, but my old carcass was not exactly looking forward to living through the three or so years it takes another baby sport horse to learn to be civilized. Well bred young sport horses are NOT LIKE ANYTHING ELSE. They have a very higly developed sense of humor, and they think things are funny that you don't think are funny, let me just leave it at that.
If you have your own farm, with plenty of big pastures, all with foal safe fences and weaning, yearling and 2 year old safe grazing (and fencing), and some other weanlings to keep the foal company after it's weaned, the costs are lower. Foals, yearlings and 2 year olds are about like wild animals. Fencing is crucial. Otherwise you're looking at boarding your weanling/yearling/2 year old at a breeding farm while it grows up. Expensive.
Even with that, though, you have to take into account various other johhny raincloud type possibilities:
1. Getting the mare in foal (especially after using them for performance, ie, not having them carry a foal for some years). Not all mares are that easy to get in foal. That means veterinary help from a reproductive type vet, and that sort of work is not cheap. It usually means getting a mare cultured and cleaned out all the time before she has the foal, and some mares will need a caslix procedure to keep their reproductive organs in good condition. It can run more than a couple thousand to get some mares in foal. My friend got her mare in foal for ten thousand dollars. Not to be a Johnny raincloud or anything...
2. Getting a foal you want to do dressage with. Not all horses, even from top dressage bloodlines, actually are suited to go up the levels in dressage. Sometimes they grow up bigger than you want, or hotter than you want, or more lethargic than you want or they have poor conformation. Sometimes they're born with crooked legs, and they don't straighten up.
A lot of people would say, if you don't have your own farm, with foal-safe pastures and fences, buy your next horse rather than trying to raise it.
Even if you start with a 3 year old, you need one more crucial element...someone to guide you in the training of the horse.