My “didn’t-even-stay-at-a-Holiday Inn Express-last-night” guess is that KSA has some nuclear deterrent now, and has had some from the moment they—allegedly—helped Pakistan finance their own nuclear program. (The idea that a nation would bankroll the development of another nation’s nuclear deterrent, yet be content to let that second nation maintain possession and control of those weapons, seems silly. IMHO, if KSA bought them, they possessed them from the outset on a 1 for 1 basis.) It will be revealed when Iran admits to possessing nuclear weapons, and not before.
Anyway, KSA’s supposed deterrent may be mateable to any of the MRBMs or modified Storm Shadows cruise missiles they possess. (Though the preceding link states that KSA and the PRC claim that WMD payloads are not capable of being used by the weapons systems KSA bought.) Or they may believe that an air dropped version from a sorta-stealthy platform like the Silent Eagles they keep toying with buying. Or if Israel’s lobbying force relents on pressuring the U.S. to not sell KSA the F-35, that platform with its ~600 nm clean configuration combat radius would certainly work for the type of counterforce strikes contemplated in such a small theater, regardless of any Iranian S-300 or -400 presence. And it’s supposed to be able to carry the B61.
The problems with the stability of this situation though are as follows:
Such a MAD paradigm is three-headed, not two, and all of the sides can reasonably fear the other two ganging up on them;
None of the sides including Israel, can believe they have a truly robust deterrent or command and control of same (though Dolphin SSGKs are probably the most survivable of any of the proposed nuclear delivery systems of any of the three sides); Israel at least has some terminal ABM defense (Arrow) of unknown capability, so it need not worry that a spurious launch warning will mean the loss of its deterrent and the death of the Jewish homeland.
AFAIK, none of the sides possess meaningful launch early warning unless the US or Russia helps out;
The battlespace is small enough that each side may not have the 30 minutes or so of decision time that we got used to during the Cold War.
All of which, again, IMHO, from a game theory POV, may disproportionately reward a first actor. At the very least, a strong threat is there. Which leads to suspicion and mistakes, and potentially an accidental war.
I am not saying that any of the three sides to this conflict wish for Armageddon to happen; I’m saying that, if all three sides obtain nuclear weapons, the situation will exist such that, in a future time of stress, with the limited information available in a crisis, rational decision makers for any of the three sides may well feel that they will be forced to use their strategic deterrent to advance their nations’ interests. I’m saying the strategic situation in that hypothetical case sounds much more unstable than the MAD paradigm between the USSR and USA, and God knows we nearly killed ourselves enough times during the 40 years of the Cold War (and a little bit beyond, if Yeltsin had felt the need to active Perimeter/Dead Hand in response to that sounding rocket.)