Iran armed houthis, so they can fight against GCC (Iran's other enemies). Houthis already served that purpose for years. Also Iran didn't come itself to their aid. Jumping into war is a whole different ball game then assisting with weapons. In return, Iran is expecting them to put their life on line and jump directly into its war which has nothing to do with houthis. Anyways, they already fired missiles at Israel and most likely are keeping its stock for later use.
Houthis were the only ones who stood for Gaza. They were viciously attacking shipping lines during genocide putting pressure that calm in red sea is via calm in Gaza. No other country including Iran did anything. Every country is selfish but Houthis are most selfless people. They can put their lives and their children lives in line for the cause they seem as just. Its their choice and its their timing whenever they'd do the next move.