Honda Odyssey all the way... I have an old one (1999) and I looooove it. Our other car is a Subaru. With good snow tires, the Odyssey handles comparably to the Subaru (when the Subaru is in all season tires - with snow tires, the Subie is like a tank). I live in a very snowy, mountain area, so I was a little nervous about the minivan, but it has been great. It is heavy, which helps, and it has a system called TCS (Traction Control System). I don't know how it works, but it kicks in when you start to lose traction and really grips the road. I'm sure the newer Odysseys have all sorts of fancy traction and stability control systems.
I only have one child (one on the way), and it is so easy to load and unload into carseats. Love the auto sliding doors, too. I hardly drive our Subaru at all now because I find it so awkward to get my DD buckled in since I've gotten bigger.