Historically I don’t think it was generally done, with the exception being the maintenance of sieges. You read about the 'campaigning season' and 'winter quarters' a lot for a reason. The weather is only part of it, the need to release your men to go home and help with the harvest is the big deal that made continuing war into winter a very rare thing. In a seige situation you had the chance to prepare in place, to build accomodation for your soldiers, to lay in supplies etc. But marching an open-field army around in deep snow? Very hard, and will desroy your army fast. Also a factor is that in winter you need MORE supplies than in summer. Your winter clothes are heavier and will be wet all the time, you need to carry or find firewood just for routine warmth for every single soldier rather than just for cooking (which can be centralised for fuel saving), and you're burning more energy pushing through snow or slogging through bogs, and keeping your body temperature up, so you need more food and you're more likely to get sick (trenchfoot, pneumonia, frostbite) so there'll be more invalids. All this means you need to transport more, and that puts greater energy demands on your troops. It's a problem that gets exponentially worse the colder it gets. Oh, and this is also an era when metalwork is hard specialised timeconsuming manual labor - so exposing all your weapons and armour to conditions in which they'll rust at the drop of a hat is problematic too. Sure, you can alleviate that somewhat through oiling and careful packing when not in use and continual maintenence - but all that requires yet more weight, equipment and time.
Of course all this presuppose a northern-Europe type climate where snow and below-freezing temperatures etc are routine in winter. But even in a more temperate/Mediterranean/Californian type climate, the harvest is still an imperative, and it's easy to underestimate how difficult travel becomes after significant rain in a time without paved roads or widespread artificial drainage (seriously, most of the modern world is built on drained swamp. Marshes, bogs, fen, and other swampy land were EVERYWHERE in pre-modern times, especially after rain). It's less impossible to wage war in a dreary morass of bog than it is in 8 ft of snow, but it's still not fun for anyone.