A fair number of people hatch chicks in winter for their own reasons. If you want chickens for a specific chicken show you might want to hatch them early enough so they are ready. The way my schedule works out with freezer space and such I normally hatch in January or February so I can get meat in the freezer before I run out. We all have our own reasons for doing things.
Some of us raise chicks outside in winter, even in your climate. If you are brooding them inside they don't care what the outside. For us to get fertile eggs in winter they have to mate in winter and they do. Some people have noticed a worst fertility rate in winter but it's usually not that bad for me. It's also a bit more challenging to collect hatching eggs in the winter in Wisconsin without them going bad because of the cold.
A hen can possibly go broody any time of the year. It is possible but for the vast majority of us it is really rare. Pullets are even more rare. Even in spring and summer you can't count on a hen going broody when you want her to. Some hens never go broody. If you are going to have any control of when you hatch or even if you ever hatch you'll need an incubator.
Another issue for you is that you often do not get good hatch rates from pullet eggs. When a pullet first starts laying her eggs are usually really small. Also the egg has to be put together pretty close to perfectly if it is going to hatch. Pullets often don't get their first eggs perfect, they sometimes have to get the bugs out of their internal egg making factory. It's fairly common to get weird eggs when pullets first start laying and that's just the stuff you can see. There are a lot of things you don't see that have to be right.
You can hatch pullet eggs and they can do OK, but I normally have a worse hatch with pullet eggs plus since the eggs are so small the chicks that hatch are pretty small. I find my mortality rate is higher with the chicks hatched from the small pullet eggs. I still hatch them but I don't expect them to do as well as they probably would if I waited a bit. I find that if the pullet has been laying about a month most of these problems go away.
To answer your question, yes they will mate in winter, though fertility can be a bit off. It is highly unlikely you will get a broody hen in winter, especially if they are pullets. If you do get a broody you can put the eggs under her but don't expect great results.
