Well, strictly speaking less than a 2:1 ratio as I couldn't get a 21 tooth gear and so went for 22 instead as I already had a 19 on, but I also write this on the off chance any other crazy fool is wondering and searching like I was and if so they aren't going to be looking for "commuting on a 1.90909 ratio".
It is actually not as crazy as it sounds. Although I had learnt from last winter that 42:19 was not low enough off-road with all the mud and slushy snow I was still a bit cautious that 2:1 would be too low for road, especially going downhills. But the added sluggishness of studded winter tyres means I'm spinning less than I would otherwise be and it doesn't feel too stupid at all; on very good days (high tyre pressure, tailwind) I might have to brake going downhills, that's all.
I'm slow and not setting any records on the road sections, but that is to be expected. On the plus side though I'm consistently slow (so far), rather than having fast days and slow days depending on the wind and surface conditions I'm just slow every day, but I can mostly compensate for that by trying to set off earlier. I was also worried I'd get too tired from all the spinning, but 2:1 isn't low enough for that to happen - afterall, road bikes have quite a few ratios below 2:1.
Off-road it is as I had hoped: really great for the mud. I have even overtaken people on geared CX bikes on some of the softer sections although they can soon catch up once we've moved past the mud. But, still, I really never thought I'd be overtaking anyone on this set-up - I hope they are suitably embarrassed.
On a related note, the only times I throw my chain seem to be with winter tyres on which is really depressing as it means a locked rear wheel and ripping loads of studs out. I thought it would be way harder to do with such a big rear cog on, but it seems this is counteracted by the extra spinning from the lower gear and the propensity for the chain to slacken sooner than I expect because of the increased rate of chain wear from all the mud. So, if any word of caution at all, don't think you can get away with a slack chain just because you've got a bigger cog on than normal.
I will hopefully remember to come back and update this post when I reach the end of winter, since we are only one third of the way through it, to confirm that the 2:1 option was a good idea.
[EDIT: 2016-03-28] Well, finally back off winter tyres and back to a 42:19 ratio, which seems a massively high ratio after being on 42:22 for some many months. And the verdict is in: As far as a ~2:1 ratio can cope with the sluggishness of winter tyres, ice, floods, 68 mph winds, snow and more mud than CX bikes can possibly dream of, then yes, I would do that again. But gears were invented for a reason. And that reason is winter. It's just too variable for one gear to cope with it all: I was overtaken at times by people in lower gears than me and I was overtaken at other times by people in higher gears than me. But I did make it to spring I suppose.