Studs are vertical. They are present to transfer the weight from the top plates (which are the top pieces that frame the wall) to the bottom plates, all of which then gets transferred to the next level down.
Beams and top plates are similar in function but beams carry more load over a wider span, and usually rest on either solid walls (foundation walls) or columns - which are functionally the same as studs but further apart and stronger.
The spacing of studs or columns is determined by the relative beam strength of the to span - or distance - covered by the beam.
So - upgrading the studs to 4x4 isn't necessarily enough - in fact just doing that could potentially be devastating if you widen them and the top plate is not able to handle the wider span. In all odds it WON'T be, but why take chances?
If you are going to widen the spacing of the studs, then I would recommend you basically build a door frame, where you have 2 2x6's installed vertically instead of the top plate (or under it), held up by 2 2x4s installed 20" apart.
That will more than compensate for any structural weakness otherwise created by the seemingly minor change.