I can't help but chime in on this...
What I own:
I have a 2010 Ford Escape V6 AWD. It's loaded with fun stuff.. most of it impractical for a bug out vehicle (other than the emergency "gear" I've added to that I actually listed in another post (my first one here) looking for advice what to add to it.
This vehicle gets around awesome in the snow, the AWD kicks in when you need it and saves you gas by not turning on when you don't. It has an automatic wheel slip control if the rear wheels cut loose and can detect slides that will automatically engage one of the rear wheel brakes in an effort to square it up. It's only kicked in a few times, but it seems to work pretty well.
The traction control however does NOT work on Sandy beaches, but there is a button to turn it off.
This vehicle has a kinda "hidden" compartment in the back where you would think a spare tire might fit, but I keep all my emergency supplies in that and a tote. There's enough in there to get me by for about three days.
To be honest, Subaru's have the absolute best AWD system for the money IMHO. It's side to side and front to back, it's really good. It's what I would be driving if only they made a Subaru that can tow 3500 pds.
Anyway, Tires.. Tires.. Tires... Snow tires in the Winter, and a good pair of all around tires for the Spring/Summer/Fall months. The new Blizzaks and WinterForce tires get as good traction with their new composite rubber compounds as you used to get with studded snow tires but they ride quite when the winter streets are dry.
Tire Chains are handy if your in the Colorado mountains in winter, but you can't drive more than 30 - 35 MPH on them (like I would want to drive faster in a snow storm in Colorado...) and are a bit of pain to put on. Might not be a terrible idea to have a two sets (front and back!), but if you've never put on a set in the middle of snowstorm, well... make sure you practice with them first!
Driver experince is probably the most important thing. I've seen big 4WD lifted trucks with kids who get excited with their first snow fall and then they realize how easily they can end up without the rubber side down.
As has been mentioned, ground clearance is a huge issue.. a high-centered 4WD is not an impossibility... I've seen it happen here in Iowa.
I've taken my Escape out into the country, in the middle of a blizzard and drove it through drifts on the road that were 2 feet high.. It would blast right through them. But I have no doubt if the snow was a consistent 24 - 36 inches, I'd be in trouble.
As a project with my son, I am working on a 1988 Ford F250 4x4. It has a 460 V8 5Spd Manual in it. The 4WD system is the old DANA manual lock-out (get out of the truck and turn the hubs) kinda 4WD. It's VERY solid and reliable. It's been fun working on it, but everytime I start the engine it costs me a $1.
... let alone drive it. Guess that'll keep him from going too far with it.
So, not much great advice in this post, but I'm feeling talkative tonight...
Here's a list of the gear I have in the Escape at this time:
Food:
Emergency Bars (Datrex) (two packs)
Emergency Water (six 1 pint packs)
Hardware:
12v Air Pump
Folding Shovel/Entrenching Tool
Hand Axe / W small Saw in Handle
LED Emergency Strobes (Super Bright - Road Emergency)
Jumper Cables
Tow Rope
Fire Extinguisher
Ice scraper
Full Windshield Sun visor
Four tie downs
MultiTool
Gorilla Tape
10 (12 hr) Chemical Light Sticks
Paper Towels
OTG Goggles
40 Channel Portable CB Radio / Extra Batteries
Stainless Steel Pot to melt snow/warm canned soup/hot chocolate
5 Inch Knife (CRKT)
Heavy duty garbage bags/ties
Water Proof Pants
Emergency Supplies:
Water Proof Matches
Fire Starters
Emergency Blanket (Soft)
Emergency Blanket (Silver/WaterProof)
Gel Burners
Battery Light Sticks (Led Flashlight/Red Strobe)
Dyno Flashlight - (Emergency Cell phone charger)
Chemical Warmers (20 count) + 2 in Plastic tote
Fix a flat
Sealed pack of wet wipes/Wet Naps
Fire Starters
Insect Repellent Wet-naps
AAA Emergency Bag (1st Aid Kit + Home of Jumper Cables and Tow Rope above)
Some items in this kit:
1 Flashlight, Batteries
Emergency Poncho
Bandaids, Alcohol Wipes, etc.
Heat Resistant Gloves
Some other misc stuff
On Person:
Zippo Lighter (Upgrading to Coleman Lighter soon)
Leatherman MultiTool
Folding PocketKnife
Smart Phone with GPS/Weather/Police Scanner/Mini LED Flashlight