This will push the Houthis to Iran. Because contrary to popular belief Iran had warned the houthis not to ally with Saleh, not to seize Sanaa, and not to move push to Aden. Iran simply wanted the Houthis to stay out of the civil war. They wanted the Houthis to simply stay in the sidelines,stockpile their weapons, and create a sort of Hezbollah style autonomous region near the Saudi border. The Houthis learned the hard way and will probably not trust no one again which means Iran moves in and have complete influence over them. Second if Hadi is smart he should provide South Yemen some from of autonomy short of independence. If not this opens another conflict. Saleh is getting old and will soon die. His sons will be the ones in control not Hadi. However the Houthis will revert back to their guerilla war against Sanaa. Yemen still has a whole host of issues but in the short term its a win for the Saudis however the Houthis will still be a major thorn on their side. This war opened the sectarian can of worms in Yemen where extremist will exploit.
I think just from the view of the proxy conflict, this development is a loss for Iran because what they can do to support the Houthis has always been limited. Unlike Lebanon, they dont have a direct pipeline to provide them any sort of material support and thats become even more difficult with the war.
Its hard to see how Hadi remains in the scene much longer, the rapid developments will leave him even more isolated and irrelevant. The Saudis are already providing air support to Saleh and welcoming his moves. If Saleh gets the Houthis out of Sana'a, Taiz, and Hodeidah they will handle him the keys to the whole car, and will have little use for Hadi. Saleh has been grooming his son Ahmed to take over for a while, he was the Ambassador to the UAE and an army general. The UAE reportedly had him under house arrest, but I bet he will be back within the next week. Ali Muhsin who was an important power broker before the Houthis took over Sana'a has also voiced support for Saleh's move. I can picture a rapprochement that gets him back in the country as well.
The South is the major elephant in the room short and long term. The UAE has been providing direct support to secessionists, who previously did not have an international backer, and majority of the South (Aden especially) is supportive of them. They were shut out of previous agreements post Arab Spring, but they will have to be acknowledged as a major player in any big resolution to the conflict. Autonomy at the very least seems to be in the cards.