Pin firing is done several ways and the term "pin firing' covers them all. Many years ago I worked on a track as a walker and exercise jocky. The whys of it I DO NOT agree with, but many track folks thought it worked.
Anyway, at one of the barns I worked at, the trainer would decide to have it done on a certain horse. Depending on what he was trying to accomplish, he might try a blistering agent first. So the groom would rub a chemical paste on the legs then wrap them, which in turn would burn the horse. More often than not the horse would stomp and rub his painful legs and get the paste all over his face, thereby burning his face too. Once time a horse rubbed his head, which was covered in the paste, on me. Hurt like h**l and blisted my skin right up.
If that didn't work, or the trainer decided to go for the harsher treatment right away, a vet would come out and plug in this nasty device with a little metal rod sticking out of it to the wall to heat up. Yup, red hot, just like a branding iron. The horse would be sedated, then burned with the red hot rod up and down the legs. Usually these things were done in the afternoons when most of the staff was gone, but one day I had to hold a horse and help out. Well, after a minute or two I handed the lead of the drugged horse to someone and ran off to toss my cookies.
The stench is unbearable and up to that point I had only heard about it, never witnessed it because the horses were always kept with standing wraps to cover everything up.
Needless to say I quit that barn and looked for one where that didn't happen. Not all race horse trainers do that, just some.
Nowadays I'm sure the liquid nitrogen method is safer (although just as painful I'm sure) but there are probably trainers who still use heat and chemicals.
Hence the name pin firing.