In closed, or endonasal, rhinoplasty all the incisions are typically made inside the nostrils. No external incisions are made whatsoever, with the uncommon exception of surgeries which include nostril-narrowing procedures such as the Weir excision or sill excision.
In open rhinoplasty, a tiny incision is made across the columella, typically in the shape of an upside-down "V" or a stairstep. If this incision is created and repaired carefully, the resultant scar should be nearly invisible. The small incision is a worthwhile tradeoff if your surgeon feels that she or he can have a greater chance of success in achieving your aesthetic and functional goals through an open approach.
Overall, scarring should not be a concern in rhinoplasty if you undergo surgery with a specialist in this area.