NY area isn't exactly cheap for horses. So board is going to be a lot regardless of how much you work off. Depending on your farrier schedule and what kind of shoeing your horse needs, I'd budget about $100-200 a month. Vet for shots, worming, check ups, boo-boos, I'd say between $500 and $7500 per year depending on how much you are competing and if your horse is arthritic at all. And then feed if it is not provided by your barn can be from $50-$150 per month. And on top of that I would have $5000 available in a slush fund for colics/major medical OR pay for insurance which is around $1000 per year depending on coverage and value (this can vary greatly). Then there's showing, training, buying tack, and more buying buying buying!! It is not an inexpensive venture, although people with more available land in their areas and even their own places and who don't compete can usually bring costs down more so than those in populated areas.
They say money doesn't buy happiness -- well happiness doesn't buy horses!