Yes, it's customary for the airline to not have to help the passenger during a weather event. And as dcpatti points out, it is even spelled out in the contract of carriage.

If the passenger wouldn't be able to absorb the cost of a weather-related delay, the passenger should have bought travel insurance. Travel insurance exists for exactly this scenario. UA even offers it during the online ticket purchase process, for 4.5% of the cost of the ticket. It can also be purchased from many third party providers. It seems that the passenger declined to purchase this insurance and is now regretting it.