In a frame with hinged joints, is it possible when i cut a piece, that if i don't have given horizontal forces GIVEN, i can assume all horizontal forces zero? Or do i have to leave that piece that gives me zero as the last piece i analyze?
You should never assume forces are zero without verifying it with an equilibrium equation. I can draw you pin-jointed frames with vertical loads only; yet balancing horizontal forces are present. A simple 3-hinged arch will do as an example; that is, two inclined rods on hinged supports, carrying a central point load.