Here in the Mid-Atlantic our winters are mild compared to yours, but I think the only difference is that the number of prime drying months is more here than there. As you probably are concerned about, you will get minimal drying in subfreezing temps. If you plan to start drying in the spring than you will get a good 6-7 months of prime drying weather. That is approximately 200 days and if you are milling 1" boards you will pretty much have lumber that is close to 12-15%, thicker lumber will of course have higher moisture content after your first season and will need at minimum another year.
As for outdoors vs indoors, for this answer I'm assuming the barn is not heated.
For wet green lumber right off the mill I would start the drying process outside. Good air flow will help the drying process and will dry the "free" water quickly from the boards. "Free" water is the moisture that is not bound by the cells within the wood. This initial drying process needs to happen relatively quickly or you could get mold growth in you lumber pile. My concern about inside a barn is you won't have enough airflow unless you have a way to get air flow to the stack. Once the "free" moisture is dried from you lumber, then the slow process of drying the bound water begins and this too is aided by good airflow. After you dry the wood outside for a season, than I would consider moving it into the barn for storage and continual seasoning, keeping it stickered of course.
BobL is correct in that drying it too quick can also be a problem. Drying wood too quickly could result in checking and splitting. So in Quebec I would just keep your stack out of direct sunlight but exposed to the prevailing winds. Fortunately you don't have the same hot desert winds BobL has.
BobL is also correct that getting a little rain on your stacked lumber is no big deal.
Now, if your barn is heated, than by moving you lumber inside for winter will mean you extend you drying "season", but I would still start the drying process outside for spring.
Here is a drying stack on my property, I leave this outside year round. I weigh down the wood with heavy cants of wood that will ultimately get cut up for firewood. The roof structure is just some 2x4s screwed to the top slabs and roofing screwed to the 2x4s. Platform is some heavy beams and 2x4s on cinder blocks.