Speak of the devil.........
We use a Snuggle pad in the pigs' outdoor haybox (they have the Pighouse/converted wooden playhouse) with the wooden haybox(it was an old bookcase carcass, about 3'x3' with a wooden 'lid' roof. ). They do wander outside the haybox for food and a nosey round but from the evidence of pee puddles and pooh nests they're all snuggling in the hay.
With a snugglepad they need the choice of whether they use it. If the space is small and they have to sit on it they risk overheating. I dispensed with the fleece cover and use newspaper to wrap it.
Hay is really good insulation but it flattens and gets soiled and damp quickly. I have to change their indoor and outdoor beds daily, the sows are prolific piddlers
( Our boar pairs were much tidier , weird for male rodents)
You'll probably find they'll be very judgey in a catcarrier- they're not nocturnal, they do alot of pooh eating at night ( nice ) and crepuscular (active dawn and dusk
) so they eat and interact . Mine sleep in the boxroom aka storage room in winter and even in a cage full of hay with two fleece blankets over the top, we hear then chattering a ripping up cardboard.
Can you get a wooden shed (eBay or Gumtree?) that you can have near the house? You'd need to make sure it's secure against foxes and the floor and roof is weatherproof .
Or a childs travelcot (takes up room but you can fold them away) for night time. You'd need to line it with newspaper and make sure there's no holes in the mesh (I'd line the inside with wire mesh with mine, chewy little toads)
Our boxroom is kept cooler than the rest of the house and they have an oil-filled radiator that I put on 30 minutes before they go out with their fresh hay and Snugglepad so they don't go from warm to cold.
If it's a garage, you can give them a nice play area but make sure you insulate it well. Our boars had to move into our garage (it's not a car garage , it's at the end of the garden) and I did worry about them (it was an emergency decamp each time) We put an old oilcloth and tarpaulin on the floor, their rabbit run filled with cardboard, newspaper,, soft straw and hay with their rubber trugs and a duvet on top of the run.
I'll come back later if I think of anything else.
Good Luck.