100%
If any customer asks you not to clean them during the winter; drop them.
It's only happened four times to me. Twice during my first winter and twice during my second.
So it's nothing to worry about. Customers will not be sacking you, just because it's Winter.
I'm quite looking forward to the cold weather; I prefer it to the sun beating down on the back of my kneck and sweating my proverbials off all the time. Oh, and no spiders and insect mess!
Also, Ian_Giles was telling me he actually earns MORE during the Winter, although I think this has a link to fewer cricket commitments.