DS was born mid-December so I feel reasonably prepared for a winter baby (was super cold the year he was born too!). I can't be doing with panic over layers so I bought a Wallaboo Fleece wrapper, for use in the pram and in the carseat going home, as it has slits for using with a harness/belts. It was great! Definitely using it again with DC2. I still dressed him, of course, but made it a bit easier as it was easier to unwrap him instead of removing from the snowsuit. He had a snowsuit, but being a newborn he slept a lot, and I found it difficult trying to remove him from the snowsuit when he was asleep. I used the snowsuit for when he was in the carrier, but we'll be using the Caboo this time around, so I think he'll have some layers, Caboo, and then me in my huge coat to cover, rather than a full on fluffy snowsuit. But we live in London and it really doesn't get cold here like it does in other parts of the country; I lived on the coast a few years back, still in the South East but the winters were awful comparatively. That's not to say babies in London don't require wrapping up 
If I recall, at home DS lived in a vest and sleepsuit for a good 3 months or so. Occasionally a long sleeved body and some crawler pants or joggers. When we went out he wore the same, but then we would put on a hat, a cardi, and wrap him up good in the Wallaboo. We had extra blankets on hand but they weren't needed. His pram also has an 'apron' (
it's a cover that clips to the pram but isn't padded like a footmuff) and a hood, and it was pretty snug in there so I think he was fine! If it was particularly chilly we had some extra warm sleepsuits, they were sort of velvety so they were a bit thicker than the standard, and we would put him in one of those. I figure we'll take the same approach with DC2! We still have all of DS' sleepsuits, vests and winter stuff.