While I could purchase the saw, I have to have a fort knox coop and run due to a huge variety of predators (including but not limited to bears, bobcat, foxes, raccoons, hawks, and dogs). So the hardware cloth for my run is already costing me $200- I've been hunting for scrap wood to no avail so far (I haven't given up yet!), but I can't go cheap on the hardware cloth or fencing. I actually looked for a used wooden play house to turn into a coop and they were also going for around $200 in my area (gotta love living near NYC- plastic was cheaper but I was concerned about wind blowing it over) so I went for my used coop. Most of the used coops are going for over $500 (new, pre-built are between $1,000-2,000) so I got lucky.I'm trying to keep my all-in cost under $500 for coop and run and it's going to be close without buying any tools.
I'm honestly glad to hear it *can* be done for cheaper though! I love reading a success story! I'm hoping I'll gain enough building experience making my run that I can build a bigger coop myself next year.
My advice on ventilation would likely not be useful since we are in S GA and we go for very open on the roost area. Heat and Ammonia are much bigger factors than Cold.
On Fencing, not sure hardware cloth is required. That stuff is expensive. Chickens are not pushers, and as long as the openings are small enough to prevent their going thru, you are better off buying fence for the predators, not the chickens. We use 2x4 welded wire and that works fine for Rhode Islands. Keeps out foxes, coyotes, bobcats and dogs. We have an 18" high run of small grade fencing at the bottom, since we do have chicks on occasion. We have a rooster. That will not be an issue with you.
Our biggest predators are Hawks and Opossums, so the top cover prevents that (yep, possums can climb fences). Not familiar with Bears at all. Would think t-poles sunk well into ground would be necessary for strength. Nothing completely stops the snakes, perhaps your cold weather will reduce snake issues, they like those eggs too. I just check the nests at the heat of the day, and keep a Grabber Stick (like used for picking up trash) to pull them off the nest.
FYI, we have 31 chickens. We use a small carport (henport) as their house with wooden fence sections to block the wind from the roosts. All that Fresh air really helps to keep them healthy.