when the roads are liable to be covered in crap, mudguards are a no-brainer. That is most of the year IME. The difference in winter is that the crap off the road is both more plentiful and likely to be highly corrosive (road salt).
Some folk ride fixed gear in winter; I sometimes do that, but more often use an IGH, fitted to a bike that will largely resist crud n'corrosion in other ways.
Both have inherently simple exposed transmission parts; keeping a derailleur system working in the winter requires a fair bit more effort IME.
cheers