Ah, my friend, that's the problem: if you call during the Big Rush, there will be waits. My guess is that between the folks like you who would normally do it themselves, but won't this time because it is too cold and the folks whose vehicles started fine yesterday when it was warm, that the guys who do the work are busier than the mythical one-arm paper hanger.
And I'm gonna guess too that they are dealing with the folks stranded in the middle of nowhere before they deal with those who merely drove home on it and are in no danger of freezing to death.
Since your bride made it home safe and sound, albeit with a ruined tire, better that they do rescue others first. They will get there in due course, I'm sure. Relax and be sure to offer them a hot cocoa when they do arrive. I'm sure they will be grateful.