I've been looking into a folding bike to help with short commutes on roads during the winter. What would be the advantages/disadvantages of a folding bike during this season? Any serious modifications to consider? Should I also consider an electric version or another bike type to help power through the snow?
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.
What would be the advantages/disadvantages of a folding bike during this season?
a big advantage is for sure that you can fold your bike and hop on the train or bus if the weather is getting too heavy. or you can leave it at your work desk (or wherever you are commuting to) if it's too snowy or rainy in the afternoon and collect it easy the day after.
Any serious modifications to consider?
you should get 'serious' tires for the winter season, some kind of knobby tires with good grip and puncture resistance. they should be a little bit wider in winter, so you can ride with lower pressure which generally results in better grip, because of the bigger bearing area of your tires.
if your bike does have v-brakes or cantilevers you should consider getting brake pads for wet conditions, they will work way better in rain & snow.
you should get good lighting for your bike, even if your commutes will be short, otherwise, you will be hard to see in snowy and dark conditions.