I'm going to give you several options: The first option is the bottom-of-the-line emergency kit. The upside is that it's all spelled out for you so you don't have to do any figuring. But it's a fairly miserly amount of food, so we'll explore other options that will give you and your loved ones more and better meals.
Following is a list for a "72-Hour Kit-in-a-Box." You can use a large shoe box, or--even better--a plastic box that has a tight fitting lid. You'll need a box for each person in your family. This information comes from an Oregon State Extension service bulletin.
72-Hour Emergency Kit
Contents:2 packages chewing gum
2 packages hot chocolate mix
1 1/2 cups trail mix
2 sticks beef jerky
2 packages apple cider mix
1 fruit juice box
4 granola bars
14 pieces hard candy
2 fruit rolls
3 packs soda crackers
1 can hearty soup (if it doesn't have a pop top, you'll need to include a can opener)
2 instant soup packets
2 liter container of water
Breakfast: 2 granola bars, 1 fruit juice box
Lunch: 1 package soup mix, 1 package soda crackers
Dinner: 1 stick beef jerky, 1 fruit roll
Snacks: 4 pieces hard candy, 3 sticks gum
Breakfast: 1/2 of the trail mix, 1 hot chocolate mix
Lunch: 1 stick beef jerky, 1 apple cider mix
Dinner: can of soup, 1 package soda crackers
Snacks: 5 pieces candy, 4 sticks gum
Breakfast: 1/2 of the trail mix, 1 apple cider mix
Lunch: 1 package soup mix, 1 package soda crackers
Dinner: 2 granola bars, 1 fruit roll, 1 hot cocoa mix
Snacks: 4 pieces candy, 3 sticks gum
Remember to rotate the food and water in your kit every year, or when any of the items go out-of-date. If you keep a list going (tape it to the inside of a kitchen cupboard) you'll be reminded when to rotate.
Now on to better things!
First of all, let's discuss water. It is recommended that you store a gallon of water per person per day. So for a 72-hour emergency kit, that's 3 gallons per person. Given that a gallon of water weighs something over 8 pounds, this is your major consideration both in terms of storage space needed, and weight. There are 55-gallon water drums available (they cost a lot!), but there's no way you could move that large of a container if you needed to evacuate. So my opinion is, stick with no bigger than 5-gallon containers (at about 40 pounds each, moving them is doable). Or buy cases of bottled water. If your containers don't keep light out, store them in a dark area away from any chemicals, fuels, etc. A closet is a good choice. Also, don't stack your water containers unless they are made to withstand the weight as they can warp and crack or give way entirely. You can live for 3 days without food, but you can't live without water, so take the time to figure out your storage in this all-important area.
Food is next on our list. Think in terms of non-perishable or long-term. Here are some ideas to help you menu plan: protein bars, dried fruit, granola, trail mix (if it includes nuts, you'll need to rotate the trail mix every 6 months or so), jerky, peanut butter, pilot bread and crackers, canned fish and meat, ready-to-eat soup, canned fruits and vegetables, canned kid meals (like Spaghetti O's), packaged oatmeal (instant flavored), dry milk powder, infant formula and foods (don't forget a bottle or two!), electrolyte drink powder packets, hot chocolate mix. Depending on what you choose to store, you'll need disposable utensils including bowls and cups, a multi-fuel stove and lighter, cooking pot(s), and a can opener. Obviously, if you don't need to evacuate, you can "shop" your pantry shelves for meals. But having this 72-hour backup is still a good idea. I home can my food in glass jars, but I still buy some cans for emergencies because they can travel without breaking.
Now that you've thought about suitable foods, you'll want to make a menu that will supply your family's needs and tailored to their personal tastes for three days. Come up with breakfast, lunch, dinner, and 2 snacks for each day. Once you have your menu figured out, it will be easy to gather your items in the correct amounts. Keep the menu list with your emergency storage so you remember what you plan to serve. It's also a good idea to write down the "good until" date for each item.
Personal items. Prescription and over-the-counter medicine (pain relievers, cold and flu meds, anti-diarrhea tablets, etc.), toilet paper and paper towels, hand sanitizer, soap in a container, feminine supplies, diapers, moistened wipes (baby wipes are a good choice), toothbrush and toothpaste, plastic garbage bags with ties for sanitation, bucket (for same). Also pack a change of clothing (including warm jackets, hats, and gloves if needed) and sturdy and comfortable walking shoes suitable for the current weather conditions. No matter what time of year it is, it's always a good idea to pack a rainproof windbreaker or poncho.
First aid kit. You can buy ready-made first aid kits, but if you choose to put your own together, remember to include bandages, ointments, antiseptic, tweezers, scissors, splints, tape, latex or vinyl gloves, tooth pain gel, children's meds, etc.
Miscellaneous but important stuff to have on hand would be things like a flashlight and weather band radio (with extra batteries--or else buy the kind that you can crank or that use solar power), whistle, sleeping bags or warm blankets, strike-anywhere matches (waterproof or in a waterproof container), multi-tool (like a Leatherman), wrench and pliers to turn off utilities, gloves, small container of unscented chlorine bleach with eyedropper for purifying water, plastic sheeting, duct tape, strong rope, saw, axe, shovel, cash (in a waterproof container), emergency contact list, medical/insurance/financial info, deck of cards or other small games.
Pets need consideration as well. If you need to evacuate, you'll want to have ready a carrier, pet food and water, litter and litter box, and any medicine your pet might need.
You can prepare a lot or a little--the choice is yours. But by giving some thought now to the possibilities, you'll be able to make rational decisions about what will be important for you and your family during an emergency.
You can even get your entire family involved in putting together a good emergency kit. Make some popcorn and hot chocolate, gather everyone around the table, and brainstorm ideas together. Have fun with it, and then kick back and enjoy those winter storms because you'll be prepared for anything they throw at you.