I have to say, I'm interested to see what others come up with, your requirements are pretty close to what would want for my next vehicle, although I don't need to worry about a family of 6.
The fit 6 requirement drives the need for a 3rd row, which usually is compatible with something that can tow, but not something that gets good MPG.
I know general advice is spend money on good snow tires and not AWD, but I love having that peice of mind, especially for me when my priority is getting to the ski slopes here in VT.
That said, my first thought was something like a Volvo XC70 with a 3rd row seat option as I'm not an SUV fan, but these only get ~20MPG highway.
On the more fuel effiecient side, I like the Jetta TDI wagon. Our 2003 GLS Sedan has been a great car, but I haven't been in a newer one. I do have a skating buddy who loved his ~2011 TDI wagon and I would expect the deseil engine to give you the ability to tow more than another car of this size, but honestly, I'm not any sort of expert on that.
Focusing on MPG and AWD, I come up with the Subaru Impreza. I'd go with the Sport Hatchback for styling. It also beats the Volvo and VW both for reliability in the TrueDelta surveys. The latter two are both "average" compared to better than average for the Subaru.
My view unfortunatley is that you're right, I don't see anything that fits all of your criteria and you'll have to try to rank what is most important to you.