I've heard before that if you tell people that you are on a diet, you will be more successful since they will "hold you to it," so to speak. It was 29 degrees F yesterday morning, but we ran. The primary reason that I packed us all up and went out was that I talk so much trash about running in all seasons and all conditions!
So, go ahead and talk a little trash about how tough you are. It is good for sticking to the plan and it is good for your ego. The key is, though, that you have to follow through. Someone might just ask you about your frigid morning run!
The other half actually does involve some money. That is buying the right clothes and equipment to keep you and your kids comfortable and safe in these extreme temperatures. Things like a wind/weather shield, mittens and even boots for the kids are key in the sub-freezing temps.
I'll see you out there...but don't be offended if I don't say hello. My eyeballs might be frozen...