My primary bike has 700 wheels. When it snows, which it rarely does, I ride, or, rather, rode, my 20" wheel Tote/Cycle.

I feel like the Tote/Cycle is more steady. Whether this is a matter of center of gravity or just the longer wheelbase, I do not know. I do know that while my body may be the largest factor in overall center of gravity, I can also shift my own weight to my advantage unlike the weight of the bike, so I still feel like a bike with a lower center of gravity can have a positive affect on stability. The counter to this feature is when I'm carrying a load. The Tote/Cycle's carrying capacity is mostly above the wheels, whereas by using panniers on my full-size bike, I can more easily keep the bike from getting top heavy. I've sent my Tote/Cycle on it's side by turning too sharply while carrying too much weight, something I wouldn't expect to happen on my full sized bike. So if I have to carry a lot, I still might prefer to be on the 700c bike.
Other factors include fatter tires on my small-wheeled bike, a low, sloped top tube that makes it easier to hop off the seat and get a foot down, and a more upright position that encourages me to look farther ahead for obstacles and again makes it easier to slip off the seat and get a foot down.

Some of these factors are not small-wheel-specific, but in my case they are what make the folder my preferred snow bike. So I'm sure that something out there should meet your requirements of both folding and being winter-friendly.