One barn I boarded at bred their 18 yr old arab, she was a maiden mare. They owned the stallion, and the two spent the summer together in a paddock. She foaled with no problems. This is not the norm, but it is possible, but they had their vet OK the breeding efforts before they started.
A farm down the road bred a 2 yr old mini mare this year. This is also not the norm. But this mare was very mature, looked and acted like a mature mare, and she was certainly more "ready" for the breeding than any mare I have ever seen. She was not ultra-sounded, and she was only bred twice. She appeared to show some signs of being in heat but nothing too tell-tale, so it will become a bit more obvious in the next few months.
NOTE: I believe(AMHR people correct me if I am wrong) that AMHR requires the mare to be a 3 year old to be bred, if the foal is to be registered. AMHA requires that the mare be 3 when the foal is born for it to be registered. Which means if you breed them as an older 2 year old, the foal will be legal(this is how I understood the rules, again, if somebody knows otherwise feel free to chime in). IMO, most 2 year olds would not be mature enough to breed anyway, but there is always an exception.