This week will be one of the busiest travel weeks of the year. Typically, we have snow in Wisconsin for Christmas and there are times that travel can be treacherous even going a few miles. We always want to get to our family’s homes and Christmas parties safely, but occasionally the unexpected happens and we get stranded or (God forbid) an accident.
For me, nothing because I keep my bag packed for winter even in Summer. I figure it’s easier having there in the bag all year long vs remember to put something back in later and if it’s summer and an item I don’t need I can always shed it.
While not really related to my bag, I do always make sure I have a field coat, hat and gloves with me when I get in the truck to go anywhere.
I also have an “extra clothes” bag in my truck that has a pair of jeans, hiking shoes, wool socks, shirt, underwear, t-shirt, sweat shirt that I keep in the back of the truck year round (keeps me from having to go on a hike in the woods in a button down, dress slacks and oxfords, lol).
Items I carry that are for cold weather: wool blanket, balaclava, big packet of hot hands.
One thing I do with my pack is keep an inventory spreadsheet of all the items in my pack. I denote items that have expiration dates and make sure I change out any items that are about to expire twice a year (June and Dec). Typically in June I pull all the items from the pack to make sure everything is holding up and nothing needs replacing.
What @JamesR said 
Difference is I always plan layers for clothing, so I can put on what’s needed for any season by adding layers. And I put a fresh stash of hand and toe warmers in once the weather turns.
Periodic restock for batteries, food, water, expired medical supplies.
Weather things like emergency mylar blankets are always in my bag so cold is not a different supply problem than hot.
What I have done, thus far, is to keep a small backpack as a general emergency bag, then I pack it into one of those large dog food containers that I keep in my trunk to keep the moisture down, and hold more winter/bulky/non essential stuff. The dog food container has things that might be helpful but could do without in the portable emergency bag, e.g. winter blanket.
Modifications are ongoing. As finances permit, I might replicate my emergency bag so I don’t have to keep putting it in and out of the vehicle.
I keep things like emergency road signs and tire flat cannisters in a different area of my trunk, as well as a flashlight and something that can break glass and cut a seatbelt in my glove box.
Examples of dog food containers:
