A folding bike for short winter commutes?
I have a 20" folder, and powering through is not something its good for.

Depending on the depth and consistency of your snow, as depth increases you'll benefit from larger wheel radius.

Spiked/studded tyres will help if you expect to ride on ice, but they're less useful on snow.  

Again dependent on conditions, but close fenders/mudguards will be the wrong thing in snow because it will pack and potentially trap your wheel.

Wider floaty knobblies for snow, with studs for ice, and ideally disk brakes will be most helpful because snow will clag up rim brakes.

Wider ranging gears will help too - most folders have a single chainring of 40-44 teeth, which limits your low gearing.

An electric bike sounds good, but you're really carrying around an extra 5-10 kilograms of mass which can contribute to slips and slides.   Adding power through wheel is also going to contribute to traction loss risks.

For snow, I'd suggest a lighter bike with wide tyres, large range cassette or a wide IGH, and disk brakes.  You can swap out the tyres for summer slicks when conditions improve.   Add lots of lights and reflectors too, and thermal clothes as required for comfort and safety.