So I tried working on getting the car to back up, which actually wasn't too bad, except I noticed that I was drifting off the driveway. I started turning the wheel over to try to line up with my parking spot beside one of the outbuildings, but it didn't do any good, I kept drifting sideways. Eventually I got stuck again, this time for good. I couldn't get anywhere forwards or backwards and my tires were starting to dig into the mud under the snow, so I just gave up, leaving my car in the middle of the lawn.
It's not a clearance issue; the lowest point on the car is the front air dam, and there's a good inch or so clearance from the snow so I'm not getting hung up on anything. The tires just don't have enough traction.
Looks like I'm not going anywhere anytime soon. Fortunately the forecast for the next week appears to be free of any more snow, and with temperatures creeping above freezing, hopefully the snow will melt enough for me to extricate myself. I suppose if worse comes to worse, I can call AAA for help.
The novelty of winter is beginning to wear thin. If I'm going to stay here for another year, I'm going to have to upgrade my differential to Positraction. If I had that, I probably wouldn't have gotten stuck. Another set of wheels with snow tires would be helpful too.