I've done boatloads of winter connections in ORD and only had a problem once, but that was due to the gate being occupied for ages, not weather and could have happened any month. DFW has never been a great one for me, but not nearly as much experience there as ORD.

I think as US Citizens I'd be fine with your connection at MIA, it's only with non-US/Canadians that it's hell because they don't have kiosks for ESTA holders, everyone gets lumped into the same long queue.