Can a closed rhinoplasty reduce nostril size?

Nostril size reduction with closed rhinoplasty? Yes but you may need other parts of your nose done to keep a balance of the parts.

Changing the nostril size (making the nostril bigger or smaller) is a procedure that can be done alone under local anesthesia or combined with a full rhinoplasty (closed or open) under general anesthesia. 
Reducing the size of the nostril is done by making an incision along the nostril base where a small incision is made to wedge out a small portion of the rim. The rim is then sutured down to the base where the nostril was previously connected to the cheek/lip area. The incision is well hidden along that junction.
When you talk about a closed versus open rhinoplasty, this is referring to the approach made to change the overall shape and appearance of the nose. An open approach uses a small incision along the columella (middle portion of the bottom of the nose) which when healed is difficult to see and practically imperceptible. In comparison, a closed approach hides the incision along the inside of the top of the nostril.