Any breed can do dressage, it's just you'll see Warmbloods in the higher levels.
If your going for 3rd,4th and Grand Prix, then I suggest a warmblood.
1st and 2nd you could choose a Thoroughbred, Warmblood, Arabian, whatever (with the conformation and training, of course). Below that, pretty much any breed will work.
Personally, I think it's more about the heart and training then the breed itself.