It depends greatly on the barn you are interested in working at. Most people looking for working students are looking for experienced dressage riders with show results at the FEI levels and that are capable of training horses to those levels. At any lower of a level it is extremely difficult to find a paying job, or even a place where you can live and board your horse for free in exchange for your work. You would probably be much better off finding a job and paying for lessons under an experienced coach. As far as for people on the east coast, Florida and California are the "dressage centers" and it will be much easier to find a coach in those places. Further north one has to look a lot harder and ask around for a good place.
If you do end up with an internship or working student position be prepared to work very hard for little to no pay. There are thousands of people vying for very few spots so only the most driven, dedicated and least partial to eating and sleeping will succeed.