Winter haircuts?

It’s our first winter with Niko and I don’t know whether I should give him his cute summer haircut or let it all grow out like a wookie. We are struggling a little to get all the mats— maybe we find one or two— but it’s not too too bad. I do notice he’s tracking more dirt and dust into the house in his fur. It’s like 9-50 degrees in the winter here— is he okay with a just a dog coat for walks if he is shaved? Even if his face and legs are also shaved? Mostly when I look up poodle cuts, people say they are great for hot summers. What about winter?