If you don't make a habit of canceling appointments last-minute. I would think 'bad weather' is like calling in sick, it happens. Once in a great while should be okay and things like tornado sirens, school closings, hurricane advisories, etc are obvious no-charge days.

If a T calls you to inquire about arriving during inclement weather, then they're most likely offering to cancel for you and should not charge you.

One time a bad storm was rolling by my T's office (there had been tornadoes in that exact spot the week before.) My T called me about an hour in advance, to see what I wanted to do because the sirens were going off around her office. Because I'm a midwest native, I knew to get there ahead of the storms and was already at a nearby coffee shop, watching the weather radar. I gave her the latest weather update and decided to stick around because it wasn't going to be to bad and would have passed by the scheduled appt. time.

I could have cancelled if I wanted that day but she wanted to give me the option.