A 3yo is of proper breeding maturity HOWEVER as a 3yo she has not completed training and therefore has no record, no points or accomplishments. I do not agree with breeding just to breed. This creates a surplus of useless horses. The only exception in my mind would be the mare was injured or unable to compete BUT had exceptional pedigree...or if you are breeding with something particular in mind. Example: I have a TB mare with no track record, show record,or anything special in her pedigree,but her conformation was flawless. She was fine boned,elegant, beautiful extentions,and great minded. I bred her to my 17hh APHA stallion with the hopes of a tall,elegant,medium boned hunter with color. I got what I wanted and now he is on his way to 2010 world show. The 2nd time I bred the 2 I didnt get exactly what I wanted but I still got a hunter type buckskin with beautiful movement. Although the mare was nothing too special I had something in mind when I bred her. I selectivly bred her...I did not go out and breed her to the first "pretty" stallion with a cheap stud fee.
I have worked on many breeding farms.(TB people dont breed past age 20 because the foals loose quality...just like with people, woman over the age of 35 have higher risks of having retarded children) I have seen mares into their 20's (25max) being bred BUT those mares are bred every year, their bodies are used to the stress. They are "factories". HOWEVER if you have an old pasture mare (18+) that is a"broodmare" then it is not fair to ask her body to do something it hasnt done before,or has done in a long time. A broodmare is in breeding condition, yes they needs breaks im not saying they dont, but breeding and foaling is what they do for a living and they are adjusted to doing it. Do not breed your mare for the first time at age 16,17,18+. Im not saying that your mare will suffer from it because many do just fine. What Im saying is it will put too much stress and strain on her body and may shorten her life or could even end it if she isnt closely watched.
Breeding carries some risk at any age. I personally know of a couple of mares bred for the first time in their late teens, with vet approval (thorough reproductive exam prior to breeding) and minor supervision, who did just fine.
However all horses' bodies age, and there is some speculation that internal structures that have not been "stretched" by carrying and delivering a foal in younger years might be somewhat more prone to injury if "stretched" for the first time as an aged mare, when those structures could be thinner, more brittle, etc. This is not a firmly established fact, nor have I seen specific studies, and it probably depends alot on the individual.
That being said, broodmares that have carried and delivered before might also have damaged or weakened areas in their internal structures BECAUSE they have carried and foaled previously, that could be more easily injured or re-injured by a subsequent pregnancy/delivery -- and they are still aging inside and out, regardless of previous pregnancies--- so the risk difference between breeding an older mare who has carried and foaled and breeding an older maiden mare could end up being a wash.
Personally, I might consider breeding a maiden mare that was up in her late teens if she had been examined and cleared by my vet. I don't think I would mess with anything 20 or over. I doubt if its a magic number, it just sounds too old
I wouldnt breed a mare period because I have no experience doing it. But I dont think I'd think about having someone breed/take care of a mare for me that was older then say 16 or 17, if she was a maiden. Its generally harder on an older horse like above posters said.