Do 4 seasons in 32mm not exist?
They do, though they may be hard to find in stock.
I'd probably be inclined to take the extra width of the GP5000. GP4S 28 came up undersized the last time I used them (26.5 mm on Open Pro).
I'd expect the GP4S to be more fairy resistant, so if you are running to a commute schedule that may swing things.
If you've the clearance, the hierarchy as far as grip on icy roads is concerned goes like...
Schwalbe Ice Spikers - knobbles with spikes (i.e. sharp studs) on - if they don't get you through, nothing will.
Studded tyres - e.g. Marathon Winter, or plain Winter (the same, but only 2 rows of studs rather than 4). Studs should be carbide rather than steel, and the more the merrier.
Proper winter tyres, like the car ones - Continental Top Contact Winter, in 37 mm (which measure at 32, if that, unless you count the mould sprues), or 42 (apparently true to size). Surprisingly good on ice - I didn't spin out until 10% on sheet ice, on a test ride one time, by which time getting off the bike was rather difficult.
An "all seasons" compound, like the GP4S.
Regular tyres.
For the first 3, rolling resistance (i.e. lack of speed) goes like the grip. Ice Spikers are very slow, Marathon Winter are fairly slow, Top Contact Winter are similar to any other similarly chunky hybrid tyre
If it's snow rather than ice, knobbles are what you want. They aren't much good on ice though, and falling on ice hurts.
A studded tyre that doesn't grip on snow may lead to lack of progress, but you are relatively unlikely to hurt yourself.
The most important thing about winter riding is to pay proper attention to the state of the road surface, and not to try to ride at normal summer-ish speeds unless you are sure the road is good.