They can't strand you at some random airport and expect you to reach your destination on your own. However, since it's weather related, you'll probably be paying your own hotel & meal charges until the trip resumes.
The announcement sounds like very poor PR on the part of the gate agent.
Originally Posted by
TrojanTraveler
Is this normal DL/DL connection policy when diverted because of weather, e.g. you're on your own to get to your final destination? I know that this isn't UA's policy...
Actually UA tried to do just that about 2.5 years ago -- dumped two planeloads of Denver-bound pax at a backwater airport in Wyoming & left without them the next day. They almost got away with it until the episode received some national media attention: