If the weather is too bad, consider postponing your journey. I always make myself aware of the weather forecast even if I am going no further than the corner shop. To dress warmly, remember that lots of thin layers work better than a few thick layers. Banish pride, vanity and fashion sense until the spring.
Make sure you are signed up with a good rescue service and your payments are up to date. Your cell phone should be topped up and working, and there is nothing wrong with carrying a blanket rolled up in the back just in case. Listen to your mother: she will tell you always to wrap up well in the cold. Take a flask of something hot if you intend to be away from any kind of supplier long. Warm dry feet are an absolute must. It is impossible to feel anything but miserable if they are wet and cold
The car may break down, of course. Sign up with the best rescue service you can afford. You can take all sorts of things in the car to help out in case of a breakdown, but everything you take will add extra weight and this may prove more of a problem in the long run. Actually you can probably leave the jacks and wrenches at home and rely on a tiny lightweight cell phone for survival. Phone your rescue service or phone the State rescue service. Be prepared to grin and bear the large bill you will have to pay afterwards. The main thing is to stay alive.
But we live in modern times. Why not let the train take the strain? There are coaches, planes and buses, even long distance taxis, with professional drivers who are trained and ready to cope with every eventuality. They have the kind of support, advice and back-up you would never be able to call upon, and their rates must be competitive. You may save money doing it yourself if all goes well, but if all does not go well, you may wish you had relied on the professionals.
Then again, if you are a total cheapskate, such as I am, then traveling in winter is the best survival trip I know. I never drive myself and I try to schedule all my long distance travels for the winter time, because that way I avoid paying heating bills at home. Travelers are always provided with a modicum of comfort and often they are given a great deal of heating, sometimes it is even too much! It is cost effective for the travel provider to lay on a decent amount of heating for a large number of people, whereas you or I might struggle to keep up the same level of luxury at home.
Even if you are driving yourself, there will be less of a saving, but overnighting at inns or hotels will still save you what you would have spent heating the home. Plus, hotel rates tend generally to be much cheaper in winter.
If you are determined to face the elements all by yourself, do have your vehicle thoroughly checked over by a reputable garage before you go, and make sure you are healthy and alert. Get lots of sleep beforehand and pack lots of warm blankets and hot beverages in vacuum flasks. Make sure there is a fully equipped first aid kit in the car and the best of luck to you!