From Foreign Policy:

The Saudi-led coalition in support of Yemen’s ousted President Hadi is supported by the US, UK, and UAE…. to a far greater extent then any possibility of Iran supporting the Houthis. While Hezbollah has greater interests in other countries such as Israel and Syria (and perhaps terrorists cells around the world), the Houthi are domestic. They care about Yemen… their home…. and they want external forces out of it.

Leaders of the Saudi-led coalition argue that they must continue the war because they cannot accept a Hezbollah-like entity on their border. If what they are referring to is a heavily armed and hostile nonstate militia on their border, that ship has sailed and the situation is only aggravated by continued war. But if the fear is an Iranian ally, they are only succeeding in pushing a group with a predominantly domestic agenda into Tehran’s arms.