Surviving a winter storm's fury can be a challenge, whether in an automobile, at home, camping, or trapped at work (Yikes!).
Back in Michigan I was without power 3-4 days in late winter due to ice storms in an all electric Condo....it sucked. No heat, no cooking, no light or refrigeration. Then the Great Blackout of 2004...same Condo without power for a week! In my opinion, one of the top priorities is alternate sources of heat and cooking! Thankfully for me, I had my supplies & camp stove from Y2K!
As in the previous posts, all those supplies suggested for your families needs in preparation for a Hurricane, war, civil unrest, or a Zombie Apocalypse will help you survive a severe winter storm! BUT...you really need those alternative heat/cooking sources!
Traveling by automobile can be dangerous in a winter storm...best advice don't do it. Even 4WD cars or trucks can get suck, particularly when driven by the untested. You need an emergency kit for the car...flares, jumper cables, fix-a-flat, starter spray, flashlights & batteries, etc. Stock water, energy bars, blankets, multi-tool, matches, etc. 365 days per year!
Everyone should try winter camping...if only for a weekend. It's fun...really! Use a 3-4 season tent, -15 degree sleeping bag, dress for the weather in layers. I did this to try out my -20 degree bag one winter at 10,000 feet in the Rocky Mountain. It was snow free & dry 10F, moon was out with a pack of Coyotes howling...great fun!
Pets...I don't have them, but you'll want to save them too...leash, food, etc. Also supplies and food for farm critters too!