I'll tell you our story about how and why we brought our pigs inside, it might help you decide it's better than just hay which isn't a great insulator.
I eventually brought my pigs in for the winter for the first time this year. This was although the hutch had a cover, as well as insulation, pigloos covered in fleece and also Snugglesafe pads (which I cannot recommend enough) - all housed in a gazebo with the sides down so no wind.
We recently invested in some cheapo thermometers from Amazon - the ones with a wire so they can tell the temp in two places - we had one measurement on top of the hutch and one inside the same area as their pigloo, and it records the lowest/highest temp too.
They're a bit like this but I think they were cheaper.
Overnight it was getting to 5c overnight but the pigloos were around 12c...but when it started getting colder overnight we bought some indoor homes (my 2 boys don't get on so we need 2 of everything!) and now they live in the dining room. We felt terrible realising we left them out last year in this cold without the Snugglesafe pads as we didn't know as much about guinea pigs then (thank you, forumites!).
We still use the thermometers in the house so we know if it's okay for us to whack the radiator up without them getting too hot.
As an added bonus, we have to walk through our dining room to get to the kitchen and bathroom so we see them a lot more and have noticed more upbeat personalities than when we saw them for only a few times a day outside. I'm really glad we did bring them in, and we know they're safe, warm and have learned the noise of veg chopping equals veggie time from the kitchen! I'm going to miss them when they go back outside!