That era's aesthetic can be strange and surreal at times, almost psychedelic.
So maybe the musician on the comic panel is feeling uncomfortable with playing this kind of gig due to the strange atmosphere, even though as any working class professional musician should say, any paying gig is good.
As knowing random facts is second nature to us trivia fans, it's easy to forget that the average person probably only knows a couple pop cultural references from the 30's.
I believe it's referring to a barn dance They were popular at the time of the strip, except in this case, the band booked a barn dance with actual barn animals. I think the drawing style looks different because this is an early one, 1981.
The top half is drawn completely different (looking like a classic far side) than the lower shaded half (looking more like an old cartoon). I'm sure the difference in drawing style has something to do with the joke, but I'm not sure how.
In the drawing, I don't think that's how Larson usually depicts cows and other animals, so I'm guessing there's some media reference or context here that we don't recognise or know.