I remember my dad talking about trace chains, single- and double-trees. Since we live in an Amish/Mennonite area, we also hear about eveners for larger groups of horses, and fore-carts to put in front of grain wagons, manure spreaders and other implements. (When scanning the classifieds around here, if you see a horse advertised as "not kid-broke" or "no ladies horse" look out!)
My dad also used to talk about sticking and tying bales, when hay balers used wire.
some terms seem very regional, too. We talk about flakes of hay out of small squares but a friend from upstate NY would talk about feeding the horses so many "sleeves" of hay
Very interesting ...
Ann