So it's going to be kinda like a native american sweat lodge thing, shapewise I mean. The inside paneling is usually aspen or alder around here, in modern saunas at least. Older ones are built from pine, mostly. Never even thought about a cedar sauna, mainly as cedar doesn't grow here, but that might be interesting. Could become a bit overwhelming when you heat it to 80C though.
I think the open floor would work just as well in your climate though. They've used similar constructions up north for ages, and there -30 or -40 isn't uncommon, with normal winter temps at around -20.
But the most important thing in a sauna is getting enough oxygen in there. One of the best saunas I've been in was just a log frame with two layers of heavy tarp wrapped around it (temporary tent sauna). We built that in the scouts when I was 15-16.
Sammy, looks good. Is that a brooder in the middle? I dig the floral fabric too. If you're adding heat tape to the nests, make the floor at an angle so that the eggs collect in one spot, that way you don't have to add so much of the heat tape.