I doubt we'll need to worry too much, but I'm of the opinion, that "knowledge is power" and that it's better to be prepared. Most of the preparing you do is fairly general and won't be wasted.
- Storing some extra food is useful if there's a heavy snow that makes it hard to get to the store or if temporarily unemployed.
- A bit of stored water can be used if your area is under a "boil order", which happens occasionally, or if the water is out on your street during water repairs.
- Planning on a way to stay warm has you ready next time the power goes out.
These are all fairly simple ways to help your family be safe and comfortable during even a minor crisis.
So, on to radiological emergencies. First remember that your safety is increased as time, distance and shielding from the source of radiation is increased. Much of the radiation that we could be exposed to has a fairly short half-life, which means that the radiation danger goes away quickly. Also, the further you are from the radiologic event, the less you'll be exposed. And, the more you can shield yourself & your family from the radiation, the better off you are.
Start with this first link which helps explain the difference between radiation exposure and contamination. It's important to understand the difference. http://www.bt.cdc.gov/radiation/contamination.asp
Next, learn about Potasium Iodine (KI) at http://www.bt.cdc.gov/radiation/ki.asp It only helps in certain situations. Too much can be harmful; the wrong types can be fatal. Don't take it unless you are advised to by authorities.
Finally, read about sheltering. I'm a little hesitant to post this particular link since it is a tad alarmist. However, I like that it shows simple ways you can shelter your family without building a 1950's bunker in your backyard. I particularly like the idea of putting shielding (bags of flour, pillowcases of dirt, mattresses...) on top of and around a stair case to use as a shelter. http://www.ki4u.com/guide.htm
My last word on this? Don't stress. Just make some simple plans and take some basic steps and you will feel safer. That feeling of preparedness is good for your health. :-)