Domestic cats are only good down to about 7°C (45°F). 2" oak has an R value of about 1.5 (2" of foam has an R value of about 12). Without a heater, neither is going to be enough

Speaking as a Fellow Moose Jockey, Depending on where you live you will need some form of heat source. Even if its radiant heat from your house could be enough in milder temps. (Build it up against the house if possible)

A basic wood shelter would be ok for "semi-cold" temps but once you drop below -10°C its going to be difficult for them to stay warm without a heat source. Even lining the walls / floors / ceiling with multi layers of old blankets will be better than nothing

Just Insulate it the best you can - wood wont be enough come -20°C - on those/any cold days, bring them inside plz.

Let the cat inside.

How many cats?

No, this would not be enough. Depending on where in Canada, you might get away with 4 to 6 hundred dollar Yeti cooler. Cut a entrance just big enough to get through through the end of the cooler, near the top. Lay some bedding, enough to add insulation and cozyness.

Honestly, though, why are the cats outside?

I never said she wouldn't be inside? She comes inside whenever she wants. She like to spend time outside so I just wanna make her a little house for when she likes to sleep outside. She has spent all her life outside, I just recently adopted her. She has a little door where she can come in whenever she wants.

Thank you, that's the kind of answer I was looking for!

Yes I will insulate it, even if it becomes bulky. Thank you!

Because she is a feral cat I just recently adopted. She has always lived outside. She can come in whenever she wants. She has her little door inside my house. However, seems like she loves spending time outside at night, I just want her to have a little cozy home outside for when she wants to or even for other feral cats I just can't adopt.

Nice comfy padded floor is essential and a thick curtain or insulated swing door to keep out the wind.

You can also look up winter pet shelter plans online with details on wind break walls, etc

You could use a Coleman cooler (the better kind) and maybe glue in a carpet tunnel or tube to the opening. You could build your box around it. That would keep it safe.

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The wording of this comment cracked me up

They make heated outdoor mats for cats. Our cats love them. If you put one inside the house it would be very warm

My neighbor used a heat lamp bulb as a heater for his dog. This might work.

In any case (not knowing your cat's cold capability) I would be inclined to put a remote outdoor thermometer in the cat house just to be sure you don't end up with a purrcycle.

Cats are weird. My in-laws have a cat that refuses to sleep inside. He used to sleep curled up under the house instead of in his bed indoors so they eventually just built him a mini kennel

My wife says “no”.

Yeah I will put foam insulated foam into it. Thanks!

Is she old enough to have lived through last winter?

Yes shes at least 3-4 yo

So I'm imagining something like a "lean-to" sitting on top of an air gap. Imagine 2x4 as "skids" and the floor laid across those skids, now there's an air gap under the floor. Air in itself is insulating.

You could use shag carpet, or old blankets/jeans/sweaters to create more air pockets inside to help with the insulation.

Then one "wall" is actually your house wall, so heat that leaks from the house will go into the cat house. You can put a kind of "baffle" inside the cat house, near the door, so there's a "room" that is cozy and doesn't have exposure to the wind. I think a heating pad, or a bulb that gives off heat, would be a good idea, but make sure any electrical stuff is rated for use outdoors.

My dog house was more or less this design (though it had four walls). And I put foam weather stripping along all the gaps. But I live in Portland, OR, and it doesn't get super cold here, so keep that in mind as you think about my suggestions.

Here's a photo of my dog house: https://imgur.com/a/ooAiM1n