My only fear about snow camping

Tire chains and a good shovel are essential items. A tow strap isn't a bad idea. Practice driving in an empty, snow covered parking lot to get good at recovering from skidding. Always check the weather forecast before heading out. Take your time, don't get in a hurry. Always make sure people know where you are going and when you will return. Pack extra provisions in case you do get snowed in so that you won't go hungry. Have fun.

I don't know how much experience you have driving on slick, snowy roads, but I've found that I very rarely need either traction control or anti-lock brakes. My Chevy Colorado has both and it is very rare to have either system activate when I'm driving on slick roads. In fact, if either does activate, it shows I'm not really driving right in the first place. And neither will save me from a truly dangerous situation if I don't drive right for slick conditions.

I drove an older small pickup for many years without either traction control or anti-lock brakes. And I drove over curvy mountain roads that were often slick in winter, but I never went off the road. Experience, carefulness, and slow braking and acceleration have a lot to do with staying on the road.

Yes, I have those conditions but not always. And I don't see them as a great problem. Sometimes I've driven over 50 miles on slick roads just to get to the trailhead. But even in winter, roads are not always slick. It depends quite a bit on whether they are plowed, sanded, etc. And it depends upon shady hillsides where the sun rarely hits the road, wind driving snow over the road, high-traffic areas and so on.

As a result, depending on the area and road, you may have slick roads or dry roads with slick stretches. Knowing the road and slowing for slick stretches helps. It also helps if there is not a lot of traffic behind you that is in a hurry. I don't let traffic push me to drive faster than I think is safe. I'd rather use a pullout and let them go around me. Or I just get stubborn and force them to get more patience.

Traction control, anti-skid, and anti-lock brakes may provide 10% of your safety, but I'd guess that 90% of your safety is your skill and experience driving on slick mountain roads, your careful choice of dates on which to drive, and your familiarity with the more likely trouble spots on the road.

Even those of us in southern Arizona have this problem. With our 9 and 10 thousand foot peaks all the hazards are present when driving to a trail head in winter on the steep narrow dirt roads leading up the backside of the ranges. More than once, on the day I have to hike back to the trail head, I've wished for more snow on that day so that there would be better traction. Or, I've timed my departure so that I reach the jeep in the mid-afternoon hoping that the ice would melt, leaving only those places on the road which have been in the shadows all day that are still ice covered.

I echo the advice that the others have given here. Get a 4-wheel drive vehicle and practice driving in snow and ice conditions. Carry tools that will help you dig and/or pull yourself out. And, have emergency provisions on hand.

I agree on the front wheel drive, the best vehicle I've ever had for snow was my Dodge caravan, driving Nor CA to Wyoming in dozens of winters, it had no problems and I never once chained up, just used all season tires. In another car with rear wheel sometimes I had to back up a steeper hill if it was icy. But snow driving isn't as scary as you think it will be, until suddenly it is, so in that snowy parking lot practice, deliberately lose control a few times and learn what that feels like. It happens fast. The best advice for snow is slow it down a bit and always have food and water and blankets in the car

Carry a bag of kitty litter in your car. It can be used for traction. I drove a Saturn Ion for 12 years and took it places it was never meant to go. Quite often it isn't the car, but the driver's skills that gets you where you want to go. Like High Sierra Fan said, "Go slow. Go slow. Go slow."

Like other have said get chains and/or snow tires(and shovel) and with proper winter driving skills you should be fine.When I lived in the mountains in an area known for its black ice I pretty much took off in every snowstorm to get first tracks at ski slopes in a multi-state mountainous area(Va/WVa/Md/Pa).My favorite vehicle was my front-wheel drive Saab SPG even though the low clearance and spoiler to aid performance didn't help in snow drifts or potholed dirt roads.I liked driving this vehicle better even in winter conditions than the 4wheel drive jeep I borrowed on occasion.

Try to drive at a constant speed not too fast or too slow where you will have to accelerate or brake too frequently.In fact,try to keep your foot off the brakes altogether and use a gentle pumping if you have to use them.And learn to correct any skids by steering in the opposite direction.When the nearby town got an infrequent snowstorm the first vehicles in the ditch were the 4wheel drives driven by people no doubt unfamiliar with winter driving skills but going too fast and feeling invincible due to the vehicle they were driving.

Your Achilles heel will be getting stuck in snow drifts versus a 4wheel drive but that is more an inconvenience than a danger as long as you are prepared(shovel/sleeping bag/cellphone/food/etc.) which you will likely be if you are going backpacking...

V-link tire chains with tensioners. These have "V"s welded on the crosschain and act as spikes.
Cum-a-long and a long tow strap. These and almost any anchor point will pull you out of anything.