Styles
There are several different styles of barn dance or hoedown, depending largely on what country the dance is being based upon. Hole in the Wall are largely a hoedown style based barn dance band. See below for different styles.
Hoedown Style
This is American by derivation. Back in the days of the mid-west dirt farmers who toiled with their horse and plough in the 1800's - the farmers, at the end of the day, would literally put their hoe's down and throw a dance with whatever instruments they had to hand - hence the name Hoedown.
Barn Dance Style
In effect, this can mean anything. It is something of a British term for a country dance or hoedown. It can be on an American or Celtic theme - or even a mixture of both.
Ceilidh Style
This is Irish or Scottish in nature and is played (usually) to traditional Irish or Scottish tunes.