Temperature: The first thing to imagine is the temperature difference. On a nice warm summer day you might find that your smoker, sitting in the sun, has an internal temperature around 100 degrees F. without a fire in it. If your target temperature is 225 degrees F. then you need a fire that will increase in smoker temperature by 125 degrees F. If, on the other hand it is a cold, overcast day the internal temperature of your smoker could be 35 degrees F., meaning you need to increase the temperature by 190 degrees F. This is near twice the temperature difference. This means better temperature control and a hotter fire with more fuel.
Wind: Now we need to think about wind. The most important thing about wind is the direction relative to your smoker. Some smokers, like the large offset smokers have a definite airflow path. Air comes into the smoker through the firebox and moves across the cooking chamber and out the stack. If the wind is blowing in this direction the increased airflow will burn your fuel faster and can cause high temperature spikes. This means keeping the vents closed down more than normal. If the wind is going in the other direction it can stop the airflow entirely and keep the heat out of your cooking chamber. It is best to let the wind add to the airflow and not stop it so if possible position your smoker so that the wind is blowing in the direction of the natural smoker airflow. It is very important to keep an eye on the wind as well as your smoking temperature.
Precipitation: Of course it's very difficult to smoke in heavy rain but cold weather also brings light rain or snow. When water hits your smoker it is going to evaporate. Evaporation pulls heat from your smoker. If, during the course of a smoke you find some rain or snow falling it is time to open up the vents and bring up the temperature to offset this heat loss. Keep a close eye on it and you should be okay.
Strategies: The ideal smoking environment is a warm and calm one. Anything you can do to provide this environment will help you maintain good temperatures and have a successful barbecue. By positioning your smoker in a sheltered (but not enclosed) space you can reduce the effects of wind. Some people have gone so far as to build wind breaks to set around their smokers to keep the wind away. This can be a good strategy but makes sure you are not putting flammable material in close proximity to your smoker. Wind can makes sparks jump a good distance.
I also know people who have used insulation materials to hold the heat in their smokers. This is okay as long as you are using flame resistant materials. You can typically find fire resistant insulation materials at your local hardware store. Some water heater blankets and furnace insulation works great. Cut it to fit around your smoker and you can hold in a great deal of the heat generated in your smoker. Just make sure you don't cover up the vents.
If the weather is bad you don't have to resist a good barbecue. I've pulled 20 hour smokes in sub-zero temperatures with great success. The secret to operating a charcoal or wood burning smoker is vigilance. When the weather is bad you have to be extra vigilant, but it is certainly doable and just because the thermometer has dropped doesn't mean you need to forget the smoker. After all, the best cure for the winter blues is a great barbecue.