ours used to be nice and warm in the hay barn....we did also provide cardboard boxes with bedding in but they didnt use them much.....we just made sure they had plenty of food and water and they always looked great and did their job by keeping the rats and mice down.....
We have cat holes cut in the doors of the various sheds and the three of them have some lovely cosy places that they frequent. Having said that, one of the "yard cats" is currently lying in front of the fire at my feet
Our adopted "never been outdoors" cats often sleep out in the stables, even in the worst weather, despite having beds indoors, and always pick the hay over any bed or rugs!
I had the same concerns as you when I first got my feral girls. I gave them umpteen cosy beds but they choose to sleep in the barn with the hay or in the stables with the horses. Cats always find a warm place.
They sort it out for themselves, I have quite a few cats, 8 tame barn cats and at least 3 'strangers' that come and go as they feel like it, one seems to live in the rafters in a hay barn.
Some sleep in the hay barns, one insists on sleeping on the seat of the tractor, one, I know, sleeps inside an old haybaler all year round, there is another one that climbs into the owners tackroom through a small gap near the ceiling and has taken up residence on the rug rack.
They all have access to the workshop (where there is always food and water) there are various boxes with bedding in there, but they sleep anywhere, on shelves, in drawers, on my saddles. In winter they often pile up together.
Love those photos nadolig! Ours wedges himself btwn hay nets on top of hay stack or on a rug especially if its fresh & warm off a horses back! Occassionally he comes in the kitchen for some aga time but has plenty of cosy options outside. Plus he has a good layer of insulation!
If they get too cold they will find themselves a nice warm back to sleep on... ours used to sleep on the top of my mare even in the snow was a monkey for it
Dont Worry Cats will always sort themselves out "Fall on Their Feet" and find a warm comfortable place my two "Strays" are now fast asleep in the House, George Over Size Polydactyl Tom asleep on his back in the dining Room and Blackie asleep on the Printer as I type this