Cheap(ish) 2 or 3 day biking adventures during winter

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What is there to do that is fun in winter and involves bikes?

I'd rather not fly somewhere warm and rent bikes because it ends up being expensive even if done on a budget.

I'd just like to ride from England. If it means I have to suck up the cold so be it but I'm looking for inspiration on fun adventures that can be done over a weekend.