Can I get a cash refund when United cancels my flight?

Yes — and the right does not depend on United agreeing to it. Federal rule requires an automatic refund to your original form of payment when the airline cancels a flight or changes it significantly and you decline the alternative offered. "Automatic" means the airline is supposed to issue it without you having to ask, and "original form of payment" rules out being quietly switched to a travel credit instead.

The rule does not care why the flight was cancelled. A weather cancellation is refunded exactly the same way a mechanical or scheduling cancellation is — the cause only affects whether United owes you meals or a hotel for a controllable disruption, never whether it owes you your money back if you choose not to fly.

A significant change is defined, not left to the airline's judgment: a departure or arrival more than three hours later domestically or six hours internationally, a different departure or arrival airport, an added connection, or a downgrade in class. Once you decline the new flight, the refund is due within seven business days for a card purchase. If United instead pushes a travel credit or lets the refund run late, the complaint goes to the DOT — airlines are shielded from most state-level consumer claims, so the Department of Transportation is the actual venue with jurisdiction.