Dave Wood on fiddle, Adam Jarrell on banjo, Brandon Holder on guitar. The recording seems to be flat of A 440.
Key of A. Some fiddlers cross tune (AEAE low to high). This tune uses chords A, D, E (the one, four, five of the A major scale). This is a square tune with a low part and a high part, each played twice (AABB structure). The low part remains on the A chord with a just speck of E chord toward the end. The high part alternates D and A chords, starting with D, and including the same speck of E toward the end. This Happy Hollow Stringband page shows the guitar chords. Both parts have the same ending phrase, though Art Stamper plays them slightly differently (with a low F# note during the low part ending only).
Art Stamper recorded the version we know [YouTube non-video]. His father, Hiram Stamper, was recorded playing something slightly different called Horse and Buggy O [Sippery Hill recording]. Read about the Stampers' Kentucky home on this National Park Service page. The old town school has a list of recordings including by Art Stamper [fast mp3] and Paul Tyler [slow mp3].
The video on this page is from a 2024 Clifftop jam [YouTube]. A smaller jam was filmed at Clifftop 2014 [YouTube]; a comment says the fiddler was Gary Sizemore.
Nora Brown on banjo, on stage with fiddler Brett Ratliff [YouTube]. She has been winning awards since she was tiny.
Professional home recording with a foot stomp. Dave Wood on fiddle, Adam Jarrell on banjo, Brandon Holder on guitar [YouTube].
An instructional video [YouTube}, played slow by 2 fiddles and a guitar.
Square dance video [tube]. Key of A. Music starts at 0:17. The band, Old Corn Lickers clarifies they will play Old Horse & Buggy, not New Horse & Buggy. The band plays the same tune for 8 minutes. This is the best square dance video we've seen because you can see how the dance aligns with the music.