If you are able to, make some sort of foundation so that the bottom of the freezer isn’t in contact with the bare ground, at all, even if it’s just setting it atop some cinder blocks.
This will help with all of the aspects you’re going to be tackling:
It will give an air pocket to vastly reduce the loss of heat from the freezer going into the much colder ground. Even a freezer isn’t a perfect insulator, and the earth is a mighty large and cold slab.
It will give space for any sort of drainage system to function better, which you’re absolutely going to want to do something for sure, as you’ll have moisture condensation and bodily fluids to content with. Even though the cats will almost certainly immediately recognize the location as shelter instead of using it for “waste disposal”, some may take some learning and/or may be too sick to regulate themselves. (I would recommend putting some sort of sloped and channeled water proofed material inside the “flooring”, to guide any standing fluid towards your drainage).
It will also help mitigate somewhat the possibility of whatever critters might be in the brush beneath before full freeze, from having an easy path into the kitty hostel.
Anthocyanins!.
Which curiously enough, can also photosynthesize, and more readily absorb energy from green light than chlorophyll!
Makes me wonder what could be achieved with some careful engineering…