When asked if I’d cancel a fitness session due to the weather (eg snow/cold) the answer is an unequivocal “NO” (unless and only unless advised to, on safety grounds). There is no reason to cancel at all. Any exercise routine can be adapted, we can dress for the weather.
We all know the phrase “There’s no such thing as bad weather, just the wrong clothing”, and the same applies when it comes to exercising outdoors. Yes, put on your longer trousers, base layers and gloves, and you’ll soon be baking hot once you get moving.
Just make sure you bring a sheet or towel to protect your car from the mud and wet on your drive home, and that hot shower will feel like the best thing ever after a tough, icy, workout!