Please do not sleep in your car overnight with it on unless you crack the windows (which you should do anyway). If you cannot sleep in the cold without running it you should not be doing it. That being said I have some experience with doing this. I would only suggest it if you have something you can flip the back seats down in. Hatchbacks and SUVs work best, but you can get by with a sedan. First, get yourself a couple yoga mats or purpose built sleeping pads for camping. If you are planning on doing this more than a few time its worth it. Most people dont think about it, but much of the cold when sleeping in a car is coming from below you, metal is cold and when you are compressing your sleeping bag you would be losing more heat from below you then above. I personally use 2 yoga mats and a thick cotton sleeping pad. Then throw on a cheap 0 deg sleeping bag. You can pick one up out of walmart for ~20-30 dollars. sleep in a hoodie, sweatpants and beanie. The beanie is key unless you want to sleep totally covered. Finally, bring as many blankets as you can fit in your car. Before you bed down, spend 30 min reading and blasting the heat as hot as you can, and try not to drink shitloads of water. Waking up at 4am to piss is brutal when its -10 out and it takes you 10 minutes to get in and out of your cocoon. Finally, crack one window of your car, more if you can bare it. This helps keep the moisture from your breath from freezing on the inside of your windows, and prevents you from suffocating. If its snowing, throw a trashbag in between the door and frame and drape it over the outside with a skipole or something to keep it held down in the wind (maybe wrapped in something so it does not ding your car). This will keep the snow outside. I suggest a nice thermos that can keep hot for 24+ hours. Although expensive, having a hot drink when you wake up in -10 below is very nice. If you are really desperate for more heat in your sleeping bag, you can use glove/boot warmers as well. If you need to run the car for short bursts, or make sure you have a couple windows vented, however this is discouraged in heavy snow, as if somehow the tailpipe gets clogged and you are asleep, you will be in a world of hurt. If you have the ability, a sheet or two to cover the windows will offer some privacy as well.
Finally on places to park, do yourself a favor and call ahead and ask the resort front desk if overnight parking is allowed, you will be surprised how many places are not cool with it. The desk staff will also be more than happy to answer you. You mentioned Vermont so I can give you 3 places that are fine. Bolton Valley does not give a fuck, and has a bar open fairly late so you can read inside and mack on the ladies till an hour or so before bed when you go to warm your car up. Mt. Snow is also totally cool with it. If you need to stay near Killington, both Killington and Pico are NOT OK with it, and will attempt to tow you, however the AMC trailhead right between the two works great, and no one will bother you, no address but its right across the street from a hotel a few miles before Pico if you are driving from killy to pico. Stowe is also, unsurprisingly not ok with it. Also be aware of where you are parking if it is snowing, as they will be plowing the lots, try to park in the least inconvenient spot for the plows, which will usually be the furthest spot from the lodge or something like that. Also bring a small shovel incase you get plowed in.
Dont be scared if this is your first time car camping. I had almost no camping experience prior to starting to do it a few seasons ago and it is one of the best decisions you can make if it is only you (I suppose 2 could work in an suv without much issue.). I managed to go down to about 15 below zero one night and was absolutely fine. Bring a few good books, load a cooler with lots of water and food that wont freeze easily and have a good time. For extended trips, a planet fitness membership will get you a shower in most major cities (only in Burlington in northern VT however) which is a massive bonus after day 2 or 3 of skiing and hanging out a bars and sleeping in your car.
If you have any more questions drop em here.
