Depends on style, particular tunes played, and the make up of the band. See recordings by Sam Morgan Band! There is some saxophone on Louis Armstrong Hot Fives and Sevens ( Jimmy Strong on "Knee Drops" for example). Recordings by Kid Thomas with Manny Paul on tenor, saxophonist Sammy Rimington, of course the great tenor man Bud Freeman playing with Eddie Condon ("Chicago" style), folks like Tom Fischer, Sarah Spencer (in England now)Brian Ogilvie and Brian Carrick are some tenor(also alto and clarinet) players in the style. Bechet of course, and Firehouse Five with George Probert on soprano sax. And then, currently leading the New Orleans "renaissance" of this music, bands like Tuba Skinny and The Shotgun Jazz Band prominently feature saxophones, playing VERY traditional New Orleans jazz. The term "dixieland" seems to have fallen out of favor, as it conjures up visions of guys in striped shirts and straw hats, and the young people in NOLA are decidely not of that "corny" ilk, yet are really playing a lot of the same repertoire faithfully, and are in fact expanding upon it creatively. See http://playing-traditional-jazz.blogspot.com for so much more on this. The gentleman above did not search youtube enough, because there are TONS of videos from New Orleans with saxophones playing trad "dixieland" music. I've played in New Orleans recently a few times, and saxophone is very welcome! tbn/clarinet/tpt is still the basic frontline, butand maybe preferred with some groups,but it is very often deviated from. Frontline of tenor, cl, and trumpet is common for example, with tenor doing some of what was traditionally tbn-the music happily is much more flexible.
Here's an example, "Sobbin Blues" the King Oliver tune, and it doesn't get more traditional than that: