A flu virus attacks and infects a cell. The cell stops normal function and begins to produce the flu virus. The cell releases the reproduced viruses to other cells. The virus incubates in the body for a day or two, multiplying in the epithelial cells that line the respiratory tract. People who inhale these droplets develop the flu.
Cold weather has nothing to do with coming down with the flu.
It is just a case of seasonal timing. Flu viruses arrive in North America in the fall and make their way across the continent during the winter.