Years later, I came across this photo post card with a nearly identical band posing with their cornets, tenor horns, "trom" horns, and "bass" horns (as termed by the leader of the SC band), along with two drums. Standing at the back right is the preacher too. The card was never posted and there is no writing on it, so it could be anywhere in the US but most likely is in the South. The stamp box is an AZO with corner triangles up and down so that gives an approximate date of 1910 to 1930. My guess is 1920 or so. The card is very faded, cracked and marked with tape residue, so I have corrected the image.
This lost musical form has a connection to the roots of jazz, but the band I heard did not play or improvise in a jazz manner. They played tunes more related to songs and dance styles of southern black churches. It was all memorized and mostly followed a formula of call and refrain, using unvarying tempos with solid march-like percussion. I remember the sousaphone was missing two button caps on the 2nd and 3rd valves, but since the player only used first valve the whole concert anyway, key changes were not important. It was definitely not dixieland but had more elements of ragtime and gospel styles. They made a wonderful kind of authentic folk music that seemed uncorrupted by any modern influences of jazz and pop music.
Did the band in this photo sound like that? Perhaps, but here they have music folios on their instruments. Were they playing a concert for a church social or perhaps it was a funeral or a wedding? Black musicians had a very restricted musical path in the 19th and first half of the 20th centuries. There was some work in circus and carnival bands, but for the most part they were excluded from theater and concert halls, and certainly so in the southern states.
The term "picnic band" is not a standard musical phrase. It's not in Wikipedia. But I think it accurately describes this kind of brass band tradition in African-American cultural life, and ought to be recognized. But finding photos and records like this are pretty rare.