Ok, so, newbie here, and might be breaking some code of conduct in commenting, but, eh....whathaveyou...
So, I live in CT. Our winters, I assume, are not as bad as yours, but, overall...makes me wish I live in the south.
A little trick I learned a few years ago, works like a champ, if your car gets stuck again. You know that spray lock-de-icer stuff? Has a funny top with an ice scraper built in? Well, if you get really good and stuck, spray a good amount of the snow BEFORE your tires. Don't spray directly under....the stuff IS flamable and all....last thing you need is a stuck car on fire. But, if you do that, it lessens the pressure of the snow on your tire, should give you the traction you need.
Were you drunk? or high? that would have made it better.