Key Items:
Water/Food: At least a few gallons of water is advisable in harsh conditions.
Fire-starting material: Flint, matches, or a lighter.
550 Cord: This gets its name from the weight it can bear. Good for making shelters, trapping animals, and treating wounds.
Blankets/Poncho
A metal container: For boiling water. It's not safe to eat mass amounts of snow off the ground. Must be a non-petrol carrying container. Kill two birds with one stone and carry a can of beans.
Tape: Electrical or gorilla duct tape has near-infinite uses.
A knife and/or multipurpose tool: Some of these actually contain a flint.
First Aid kit
Compass
A mirror: For signaling. In a pinch, a makeup mirror will suffice.
Pocket sewing kit
Essential Tips:
Planning: First you have to assemble your kit. If it's mobile, make sure it's kept in a water proof container or bag.
As for the first 24 hours of being lost or stuck:
Shelter: If you're in a car, don't leave it. If you're on foot, build a shelter, or find one: Finding shelter is the paramount consideration when stranded in extreme weather.
Hollowed-out logs can be cleaned out and enhanced. Caves work as well. Reduced living space means warmer living space. Beware of occupying animals, and consider ventilation.
Here's an example of a snow cave, dug from beneath a tree caught in a snowdrift:
http://static6.businessinsider.com/image/5668488384307623008b8932-840-637/survival2.jpg
Start a fire: And plan to maintain that fire. Dig a hole and use dry pencil-thick branches and evergreen limbs as kindling. Evergreens burn fast and hot.
Fuel should be thicker limbs that have broken off a tree — found near the ground, but not submerged in snow.