I normally pack up the smoker and turn to stews and slow cooker recipes, clearing out the meat I smoked during nicer days, but I had to take my dad's new smoker for a spin in Fargo, ND over the holidays. Based on that limited experience, the main difference seemed to be the quantity of charcoal I needed to fight against the ambient single digit temps. Unsurprisingly, it also took longer to get the temperature up initially.
Other than that, there didn't seem to be a major difference in the process, time, or results.