For most of my winter commuting seasons I've used a derailleur based drive train. Virtually every year I'd have some issues with shifting. Further I've been unhappy with the amount of maintenance it took to keep the chain in halfway decent shape. Every spring I'd end up pulling the derailleurs off the bike to clean them up. Lots of grit in the jockey pulleys and pivots. This with full fenders and a generous front mud flap.
So I decided to try an IGH starting last winter. Well, last winter was about the wimpiest I can ever remember so it didn't count.
This year has been more typical. Not much snow in January but we had decent amounts in December and February. I've had no real shifting problems to speak of. I also used a rust resistant chain this year. It's stayed pretty much rust free and I've only lubed it twice so far this winter. I've used the same chains in the past but they were marginal with an 8 speed drive train and I couldn't find any available at the time that would work with 9 speed. Now I think you can get them. Regardless, I think using an IGH vs a derailleur has allowed the lube to last longer.
A couple of pictures are below. The first is the bike I was using a couple of years ago. I probably had just cleaned up the chain and relubed it less than a week prior to taking the picture. Once you get into a wet part of the winter where there is thawing and refreezing the chain seems to lose the lubricant pretty quickly.
The white spots on each bike is salt residue.
The IGH does have its downsides. I do notice the wider spacing between gears and there's a noticeable drag in colder weather. I plan on switching to oil lubrication next winter which I hope will alleviate some of that.