That could happen in a low fuel situation (it's happened to me twice). In both cases, my destination airports shut down, and we circled hoping they would open up. When we got low on fuel, we were diverted to alternate airports. A JFK flight was diverted to Stewart, and an ORD flight was diverted to Des Moines. That's 2 flights in well over 1.5 million miles of flying. I think the odds are with you that you'll land on time, as scheduled.

The last two winters I did a bunch of mileage runs into MSP (like -20 every trip I got there) and OMA. Never a problem, even with snow coming down about every other trip. Just watch the weather reports. Your only concern should be if a major storm is coming through, in which case your carrier may let you reschedule to before or after the storm.