Glad that was resolved so well! BFbob sounds like a thoughtful person.
I am another who detests driving in horrible weather. I am good at it, but I hate doing so, more than almost anything else in this world. There is something so unsettling about not being able to trust what's beneath one's tires, and that feeling of having so little control is, I think, what causes me so much stress.
That said, if I had been in the OP's daughter's situation, I think I would have explained that I didn't feel comfortable picking them up when the weather was so awful. Also, I don't believe she should have felt obligated to reimburse for the cost of a cab, (although, offering would be a nice thing to do, and I might have done so, in her situation, obligated or not.)
One of the worst white-knuckle rides I ever experienced was when I had been out of college for about 7 years, and a friend from down home flew up to visit. I drove to the airport to pick him up, and it was only snowing lightly, but with a lead-colored sky overhead promising much worse. Sure enough, by the time he landed and we headed back to my town, it was snowing so hard I could barely see and the roads were icy. What an introduction to the "great white north" that was for him!