We aren’t made of candy gloss you know.

If you don’t like working in the rain, and don’t mind losing income, then don’t work.
If you’d rather have the money in your pocket, and choose yourself to have time off when you choose, rather than being forced to have the rainy days off..,,. Just crack on.
Train your customers, they won’t care in the end. It’s your business.
Like Daz says, if it affected the quality of our work, then what happens when you get a wet day just after you’ve been, or a wet afternoon?
This is the UK, it rains all the time.