The weather is unfavorable for the interview.

You mean you don't have enough money and time to buy clothes and stand in front of the interviewer with dignity. If I were you, I would make sure that my clothes are only wet and not dirty, and then call the interviewer before entering the coffee shop to briefly explain the special situation and prepare him mentally. If he asks, explain more. If he doesn't ask, don't mention it yourself. Say the theme.