I'd like it if people complained if you walked into a tavern late at night and let a cold gust of air into the place, and the fire should flicker some from the wind. People should also put on heavier clothing for the winter, including you. There can be winterized forms of the armor with extra fur to keep you from freezing, and cloaks/capes to warm you. People around town can wear heavier coats in the cold weather months or during a snow, and could be seen outside clearing the snow from the front of their business.
On a more extreme high mountain town, people could be walking out of the second story balconies right onto the heavy snow with their snowshoes on because it piled up that high. And have people talk about stocking up for winter, with shops curiously busy in the fall. What sort of indications of weather would you like to see represented in the game?