Hi FiddleFye-
I built three cat houses last fall, and have used them for a year. They're three different designs, though none have forced-air heating like you're considering. Still, maybe some of my experience might give you some ideas. I'm in St. Louis, MO, so the winters get below freezing (occasionally below zero), and we have a good amount of snow, but not as much and not as cold and not for as long as when I lived in Chicago!
A quick background story: My wife and I ended up taking responsibility for two litters of feral cats. Our neighbor was feeding the pregnant mama cat, she had a litter of 4 kittens (on April 1st of last year), and then told us they were going to get her spade. Unfortunately they did not, and so when the second litter of 5 more cats came along (on August 28th of last year), we took charge and had her spade, and got all the kitties fixed over time.
[Flash forward: Over the past year or so, five have become very socialized, friendly, and loving, and are very part of our family. They spent about 50% of the time inside. Three seem to have moved on. (We had some clashes between siblings, and at some point they each individually just stopped coming to the yard, which was very sad.) We also still have two feral fully-outdoor cats (mama, and one kitten from the second litter).]
However, in the late fall of last year I began to realize I would need to house 9 kittens of varying ages over the winter who were growing quickly. In the beginning, 5 kittens slept in a pile in one tiny little store-bought cat house. But that time passed quickly! And due to some conflicts, and ever-changing allegiances, I decided I needed more than one house to give everyone room to be safe in the cold and to have alternative places in the case of two cats being unhappy with one another. I also decided that I was unhappy with most (all) commercial offerings, as they were insufficiently insulated. Even the fancy Etsy houses had poor insulation.
My design criteria were based on the idea that I wanted a fully insulated enclosure (insulation on all six-sides). For the first house, I decided on a box-within-a-box style, with 2" Foamular hard pink foam insulation on all sides. I wanted it to look nice, so I made it out of cedar. I clamped and glued planks together to make the walls and roof. The inner box was made with 1/2" baltic birch plywood left over from a speaker project. I built a stand to elevate it above ground. [Pictures attached.] Then we added a K&H heating pad for cats inside. With the 2" insulation on all sides (top included, though not pictured here) the house stays _very_ warm even in the coldest of nights. The cats use it in all sorts of weather, but if it gets above about 45-50F, we turn the heating pad off. (When it's that warm, they prefer to sit outside on the heating pads on the chairs. Spoiled cats :-)
Since the first house was a success, but we clearly needed more room, I planned the second house. I discovered I'm very allergic to cedar dust, so I didn't want to make another from cedar. I had some very good exterior paint on hand (Sherwin Williams Emerald Urethane Trim Enamel) and so I decided to try painted plywood for the second house. Same general design, box within a box with 2" insulation on every side. The outside was made with 3/4 exterior grade ply. The inner box was made with AC sanded 1/2" ply. But some upgrades: I made this one two-story for more room and separate spaces, increased the slope of the roof (good call), and added a roofing membrane on top (very good call) along with drip edges made from aluminum angle. [Pictures attached, sorry not too many of this build.] The roofing membrace was 12" wide, and placed with overlap of about 1" with the seams going downhill. Verdict? This house is just as warm, but still looks brand new after a year. The drop edge may have been overkill.
The polyurethane-coated cedar on the first house didn't weather well. It mostly wore off after a year. The cedar is fine, of course, but it is getting grayer. I will resand and recoat the cedar with Penofin oil finish next spring/summer. That tends to last about 2 years before needing a refresh based on a cedar gate I built. I did add roofing membrane to the cedar house this summer, and that solved the tiny leaks I got through the roof glue joints. The roofing membrane is amazing.
roofing membrane:
Finally, we decided we needed a third house due to above mentioned conflicts between some kitties. But it was late in the season, already cold, and I needed to build this one fast. I was looking at our deck box, and decided it could make an excellent version of this cat house, and be fast to implement. I did scale back a bit - I decided the inner box was really unneccessary, as the heating pads wrap up the sides, so the inner box never even got dirty or worn. I got a second Keter deck box (from Sam's Club, but they're available multiple places.) The box design is such that you can add the 2" of insulation, and cut holes in the ends, and it has tons of room for multiple cats. I put a divider in the middle with a door, so the cats could have two separate spaces inside, and also a second way out. [Pictures attached.] The other houses took about two weeks to build and finish. This one was done in two evenings. We added two of the largest size K&H Lectro Soft heating pads. Verdict? This is the warmest house, predominantly because it has two heating pads inside it. Stays perfectly dry inside, and the doorways (although not fancy at all) don't seem to be an issue for getting in or out. We run the cords for the heating pads through the doorway, and put them on an iPhone-controllable outlet for easy control (this is true for all the houses).
deck box:
heating pads:
So, all in all, if you don't mind the look of the deck box, it's the winner. It's just as good (and warmer) as any of the other two, has two separate spaces, and was much much faster to build. Cost less than the cedar house too. Let me know if you have any questions!