I'm in the cutting camp actually. You have to be more careful and you have to master the "up cut" to make it look good. My boys mane isn't super thick so pulling it could make it too thin. I'm with NBEventer, go back after you cut it then pull as needed to make it look good.
That said, if your horses mane is thick (which it looks like it may be) then pulling totally the way to go.
As for the length, I was taught 4 fingers if you are doing button braids. It looks super short to me when it's done!