Iran sees this as a threat because they believe it will harm their other strategic interests. Iran can't directly target Saudi Arabia since US would wage war on Iran in that case. So it could only do it through proxy means. And Houthis would have played a great role in that if they agreed to strategic agreement with Iran after they secured majority of Yemen. And this probably would have happened if Houthis had time.
But, Saudi Arabia blew that chance but taking action as soon as Houthis took over northern Aden. Saudi Arabia dealt a strategic blow with the timing. Now what Saudi can do is keep up air strikes, and wait for Pro-Hadi forces to regain Taiz and Lahj provinces. Then give them new supply of arms to keep defend. If it can secure that. Than Saudi Arabia can now direct attention at Syria. Which is what scares Iran. Especially if Turkey backs it. Problem is if Russia will do anything. Honestly imo Russia has more important things such as Ukraine and Baltics. It will not risk regional if not world war over an arab entity it has no historical connections with. So Saudi Arabia and this coalition can expand their moves and go for it once and all. No fly zone in Syria and air strikes will mean quick takeover of Syria. Since the opposition there is much more expericned/well trained than the tribes in Yemen.
Iran will not be able to react in any way unless it gets backing from Russia or China. It needs to quickly secure strategic agreement with them. If Iran doesn't act in Yemen, it's other strategic interests will be harmed. So it either sits and watches, or does strategic agreement with superpower that will send its navy to mandab strait or it directly targets Saudi Arabia and ignites world war that will draw everybody. If Iran watches, pressure in nuclear talks will increase. So depending on how desperate Iran gets, we won't know until then if it will target Saudi Arabia. And we don't know if Shia population of Saudi Arabia will revolt. But things from strategicshort term are looking bad. Long term it's too early to tell.
Bottomline is US/Russia won't get involved except either attack on Saudi or Iran. So it leaves the region in its own fight. With Iran not able to play much cards and with Saudi securing alliance that surprised the world. Even if symbolic at this point. It isn't symbolic for Arab nations. Especially Egyptian involvement.
Very risky decisions to make by Iranian command if Saudi Arabia gets decisive victory in Yemen and does what I stated in first paragraph. It needs to take advantage of situation, don't just try dealing a blow to Houthis. Make sure you do more now if you want to make the most gains and severely weaken Iran's position. If Saudi Arabia doesn't do what I stated, this won't harm Iran or Houthis much(unless blockade on sea keeps remaining).
This is just political analysis. Not choosing sides or encouraging something. Just stating both sides options.