Cosmetic surgery as it relates to reconstructive aspect can be done at any age. Certain conditions that require reconstructive surgery such as otoplasty (pinning back of protruding ears) can be done as young as 5. Aesthetic enhancement surgeries on individuals should be delayed till they are 18 years old.
Rhinoplasty might present one exception as it can be done during teenage years. In Otoplasty and Rhinoplasty the usual concerns are not achieving a greater beauty but to avoid certain social issues such as kids making fun, bullying, lack of social attention because of a very large nose etc.
After becoming an adult the age becomes less relevant in deciding who is a good candidate for cosmetic surgery. The more important factors are the physical and mental health of the individual. Surgery is a stressful process on the body and mind. A good candidate is someone who is physically fit and sound in mind with no self esteem or body image issues. After the age of 40 the likelihood of developing a serious medical condition like stroke, heart attack, diabetes, high blood pressure starts going up.
Based on age, there are certain guidelines that address the possible need for preoperative medical clearance from your primary care physician. These might include getting an electrocardiogram, some blood work and physical exam by your doctor. The sicker you are the more tests you will need. In certain cases you might be denied surgery as the risk to your well being might be too high.
In summary, age is not a limiting factor when it comes to cosmetic surgery but health both physical and mental can be.