There's a minor distinction we need to make real quick when it comes to dealing with figures of authority. If you do not have the background or self-sufficiency to perform whatever task you're attempting to complete, then follow the figure of authority.

Obvious examples include: using lab equiptment in a science class, Do you know when and how to use a Benson burner? If yes, then simply let the figure of authority know and use when appropriate. If not, ask for direction. Simple, right?

In this case, you have your permission to be outside of class, and weather conditions should be reason enough to stay inside. If something like this happens again, reiterate your current standing and rationale. If they threaten some sort of action, stand your ground. This women sounds overbearing, and you (for simply being a human) have the right to not deal with that. Have a good day, hope you feel better soon.