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