For a long time misguided commentators have ignored Yemen's history to paint this conflict as a proxy war between the region's two beasts, Iran and Saudi Arabia. This is understandable- great power meddling is much easier and a more gripping story than something as idiosyncratic as Yemen. Unfortunately, this was also: wrong. Or at least based on little-to-no evidence. The government made the choice to run with this, to encourage and promote it (the Iran side, anyway) because it helped to tie the battle into a larger regional picture, and put him on the same side as the US.
Things have a way of slipping out of control, though. Saudi Arabia entering Yemen has had the weird effect of rallying people against Saudi Arabia, but also might make Iran have to help out the Huthis, if only to save face. They can't, after all, let the Saudi's "win" the "proxy war" between them. Perception is reality. This is true everywhere; please don't read this as "in the Middle East, only force is blah blah blah".
I couldn't see a good reason for Saudi Arabia to intervene. I think it was near lunacy, as they don't really have anything to gain, and a lot to lose. And their mistake is compounded by the way it might force Iran's hand. This is a very good example of the consequences of doing something that seems good for the moment- talking about Persian adventurism is your country- without thinking down the road. Minus the specifics, that last sentence could be used for nearly everything in Yemen.