Specifically for winter, I add the following to my car:

-snow tires
-snow brush and scraper
-bucket and grain shovel
-extra hat, mitts, wool socks and sweater for everyone
-complete change of clothes for the wee ones
-couple of wool blankets
-chemical hand warmers
-flashlight and extra batteries
-fire starting kit
-couple of SS water bottles
-instant coffee and koolaid
-high fat ready to eat snacks (nuts, fruit, chocolate, etc.)
-a Mountain House meal
-hi-viz vest and toque
-insulated mechanics gloves
-extra pair of boots for me
-jug of winter anti-freeze
-bag of kitty litter or salt
-road flares
-small backpacking tent, blue tarp and some paracord
-extra bic lighter
-extra plastic bags

*Everyone starts bringing their winter coats and snow pants at this time of year too!

My purse also gets beefed up at this time of year:

-extra hat, mitts, socks and buff for myself and my daughter
-my good winter mitts
-esbit emergency stove and tabs
-SS water bottle
-couple of clif bars
-couple packs of instant oatmeal
-instant coffee and koolaid
-chemical hand warmers
-extra heat sheet or SOL emergency bivvy
-extra BIC lighter
-extra plastic bags
-fire starting kit
-a couple of tea lights