I commute (5 flat miles each way) and do general errands on an old 5 speed steel bike, got it from a bike recycling place. It has mudguards and clearance for the ice tyres that go on it come mid October. It has V-brakes.
There has been no issues in 3 winters, apart from the chain seized once because I neglected to throw a bucket of water on the drivetrain after riding in road salt. Changed the bottom bracket last year, front brake cable and serviced headset this year, I have been using the bike with a different wheelset in summer too, so not all of the repairs are because of winter riding.
I ride to work in any weather, even snow: as long as you don't leave grit on the chain for days on end and clean your rims every couple of days - a quick wipe will do - this kind of bike is simple to maintain.
5 gears are plenty on the flat (I'm certainly not the strongest rider, still, mostly use the one gear

), this option would leave you lots to put towards the next shiny summer bike.