It may be cold and your fingers numb, but you must still take the time to clear your windscreen completely. You're breaking the law if you don't, but more importantly it's far safer because you'll be able to see out more easily.
You should also make sure the side windows, door mirrors and the rear screen are clear. Get a decent scraper and a can of de-icer - it'll make your life a whole lot easier.
You also need to make sure your car is ready for the cold weather. That includes checking things such as the anti-freeze in your engine's cooling system. Make sure you have the right concentration of windscreen washer fluid (and that it's fully topped up), and check that your headlights and brakelights work properly.
Older car batteries suffer in cold weather; many garages offer free health checks for them. If your car battery can be topped up, make sure the plates inside are covered with water - only ever top up the acid cells with deionised water (available from any motor accessory shop).
Consider having your car serviced before the winter to ensure it's in the best shape possible. Check your tyres are properly inflated and that their tread is well above the legal minimum.