Hoof wrestling
Hoof wrestling is a type of wrestling where two individuals wrestle using only their hooves. The sport is quite popular among athletic and show-offy ponies.
History
Applejack hoof-wrestled Rainbow Dash once, but when Dash almost beat her, she cheated by giving her Apple Cider, distracting her[1]
Fluttershy "defeated" a love-struck pony in order to get information about Shadow Lock.[2]