Quebec was easily the coldest place we visited. Our first day was a real shock to the system, after a couple of hours walking along the Governor's Promenade and gazing at the Chateau Frontenac we had to race into a restaurant to warm up before heading home to throw on a dozen more layers! It was so cold that after a few hours I couldn't take any more photos my camera's battery would refuse to turn on. So yeah, cooold.
But the cold had the added advantage of lots of snow, and the prettiest snow I've ever seen. It must have snowed earlier in the day that we arrived because it was all so clean and white and deep. If we'd been better organised I would have arranged for us to go dog-sledding or out to a neighbouring town like Portneuf, but I kind of liked spending our time sleeping in and lazily walking around before spending hours in cafes and bars.
Vieux Quebec (Old Quebec) is really charming and was only a short walk from where we were staying. It does get quite touristy (LOTS of souvenir shops) but it's also where a lot of the museums and quaint chocolate shops are, so it's almost impossible to pass up. The restaurants did seem a bit pricey so we mostly ate outside of the fortifications and just came down to enjoy the view over the icy Saint-Lawrence River and the cobblestoned streets. Those streets were crazy icy and steep though. I was sure either Tom or I would fall at some point,* so I was clutching onto any handrails I could find. There's an amazing place in the Old Town shopping streets called La Fudgerie which, you guessed it, makes fudge. The little store is full of all these different varieties - some sold in huge blocks, some dangling from the ceiling like fudge salami - and Tom and I went a little nuts trying samples and buying a bunch of fudge and chocolate to bring home as gifts. Another great place to visit is the Morrin Centre. It was originally built as military barracks before being turned into a jail, then a college and now a beautiful library. You can still visit the cells from when it was a prison - but not during the winter. Unfortunately I had to content myself with a beautiful old building and piles and piles of books /sarcasm.
Timing wise, if you're thinking of a winter trip to Quebec you're probably better off visiting in February. December is definitely their off season so the streets were empty and there weren't very many activities outside of the museums available. But if you come in February you get the beautiful snow plus their winter festival, the ice hotel and a lot more winter related fun. But if you'd rather make the most of the cheap accommodation (Auberge Du Quartier gets my recommendation) and are happy to just visit cafes and museums (which, let's be honest, is a brilliant way to spend a holiday) then December is actually kind of perfect. Plus you get those Christmas happy feelings with all of the lights and snow and outdoor santas on display.
Also, a good thing to do would learn some French. It hadn't really occurred to me how much French there's be in Quebec. That sounds super ignorant of me (and it was), but I had just assumed everyone would be bilingual so my 'bonjour' 'bonsoir' 'oui' 'salut' would be enough. Turns out French is the mother tongue of 97% of people in Quebec and only a small percentage actually speak both English and French. So while there was usually at least one person who could speak English wherever we went it really wouldn't hurt to know at least some basic phrases before you head off to explore the city.
*I did eventually but that was from pure clumsiness on a flat and non-icy street corner!