One big tip for rebooking: Have a good phone and many many numbers.
ORD is UA's big hub and when it is hit by snow, lines/queues will be long, physically or telephonically.
Do you speak Chinese? UA has Mandarin and Cantonese US toll-free numbers, in addition to other languages. They might not be 24-hour, but still may not be affected by the long wait times.
Can you find a way to call abroad? Keep UA's foreign reservation numbers ready. They will be even less likely have long waits.
Can you solicit help from friends and family faraway? They may help you get things done more easily (and maybe more cheaply, them calling their local number).
My mom once had her HKG-SFO plane broke down in SGN, and the HKG check-in counters had long lines. I was at the office that evening so I had access to three phones, calling UA's English and Cantonese lines waiting one phone to each ear and her on speaker! Finally English agent answered first and got her on OZ HKG-ICN-LAX. If she had stood in line for two hours, that option would've disappeared. Going back to grandma's house and back for next day's flight would've cost her US$26 already!