Part of it depends on what you call winter. Winter in Houston is different than winter in Minneapolis.
Part of it depends on if you also use a car.
Part of it depends on if you consider your bike art or a tool.
A typical winter here means at least a little snow every day from mid-December to mid-March. I don't own a car and the last time I took the bus to work was one day in July 2006. Although they live in my living room and have to be kept cleaner than most other people's bikes, my bikes are tools.
I ride my primary commuter, a 2006 Trek Portland, in all seasons and all conditions.
It's essentially a CX bike with a little bit of touring bike DNA. For winter I put on the Nokian Hakkapeliitta W106 snow tires (in 35mm), wider fenders to cover the wider tires, and swap my cassette from a 12-23 to a 12-27, and ride.
In six winters, the only thing other than typical wear items I've had to deal with was corrosion in the disc brake calipers. After cleaning them up, I reassembled with a lot of anti-sieze, and haven't had to touch them in three winters.
Plan on replacing your chain and recabling in the spring. If you have rim brakes, switch to KoolStop salmons, and keep a couple of extra sets in stock. Keep an eye on the brake track of your rims, and have at it. Before winter, grease (or use anti-seize on) all the screws and fasteners on the bike. Those are things you'll need to do no matter what bike you ride through winter, unless your plan is to have one you simply junk in the spring.
The primary disadvantage I see to the folding bike you're looking at is that there aren't very many studded stow tires made in 20 inch--although that may not be an issue for you.
The primary advantages I see to riding my best bike through the winter is that when the conditions get dicey, I'm already on a bike that I'm intimately familiar with, that I know exactly how it handles and responds, and I don't have to keep a separate stock of spare parts.