Well, the whole Houthi/Iran thing is overblown anyway. Yes, there's elements of support and sympathy, but it's very low key and mostly brought up to suggest the Houthis are not a legitimate political force in Yemen, which they absolutely are.
Iran does have short-range precision missiles, but we're talking the kind of ranges where they would have to be fired from inside Iraq to hit Saudi Arabia, and even then it'd be a stretch. If they did do that, it would implicate the Iranian-aligned elements of the Popular Mobilisation Forces, the government-backed militias who fought ISIS and subsequently were rolled into the Iraqi security structure.
Which would mean another Iraqi civil war. KSA and the USA would tell them to stand down and lean on the Iraqi government to make it happen, but the PMF are popular because they did fight ISIS...and that would be on top of any Iranian conflict.
And if they launched the missile from Iran itself, then someone has been upgrading their missiles from earlier on this year. Which means someone has been naughty. I'm not so sure Russia would provide Iran with advanced missile technology...I never got the impression that Russia fully trusted Iran that closely and the S-300 system was already a significant gift to Tehran.