Housing, Opportunity, Mobility, and Equity Act of 2022 This bill addresses zoning policies, housing affordability, and economic security. Specifically, the bill requires each state or local government that receives a Community Development Block Grant from the Department of Housing and Urban Development or a Surface Transportation Block Grant from the Department of Transportation to develop and implement a strategy to support zoning policies or regulatory initiatives that create a more affordable, elastic, and diverse housing supply. Additionally, the bill establishes a tax credit for individuals who spend more than 30% of their adjusted gross income on rent and requires the Department of the Treasury to make advance payments of this credit to eligible taxpayers who elect that option. The bill also requires Treasury to establish a Rainy Day Savings Program to allow an eligible taxpayer to defer 20% of the amount that would otherwise be refunded to the taxpayer. Treasury must invest the deferred amount and later disburse that amount, along with any interest, to the taxpayer.