At a local, "let's give it a try" show you may find a variety of breeds but when points and money is on the line you will only see QH and, to a much lesser number, Paints. Those horses are specifically bred for the job.
That is not to say that an Arab or TWH hasn't done cutting and maybe they were even good at it, beating QH at the local level but they just never make it to the statewide level or beyond. As a breed, they just don't have the build or cow sense that has been bred into the QH.
The right tool for the job - you can pound in a nail with a pliers, but a hammer does a better job.
I think if they were really good at it you'd see them in big competitions. All the cutting trainers I know could care less about the breed of horse their big concern is getting to the pay window. Their going to take the horses that get them there.
Well I've only seen qhs but I bet theres alot of other breeds that do it...idont really watch lower levels of cutting so I wouldnt know but theres bound to be other breeds. Personally I think qhs work best with the cows because they r built for it.and they are smart and quick.