Hi lego mine are in and out pigs.
I bring them inside for Guy Fawkes weekend because of the noise. They have a wooden playhouse for outdoor living.
We put ours in the dining room on the first winter but my (at the time) two boars got very arsey in their cage, we had to divide them. I put them in the Pighouse by day with a little heater or Snugglepads and fresh hay.
Important thing is to keep them dry and the temperature constant.
Now ours have winter nights in the small bedroom. There's no door, we can switch the radiator off and open the window a cm to give ventilation.
I like them to go out in the Pighhouse as they can forage about in hay and their playtunnels. Indoors they have hay in a trug or a rack to keep it from travelling . They have fleece or towels but it seems a bit un-natural.
With the storeroom, can you leave the kitchen door open so they can get a bit of residual heat - and be prepared for them being noisy when they hear you open the fridge or rustle paper 
There's lots of ways to insulate them. Fresh hay is warm, I put soft straw at the back in some newspaper (not for piglets but I fond the straw is softer than alot of the hay and it doesn't flatten).
An old duvet over the cage
Cardboard over the cage.
There is no holy grail of bedding
it's a case of trial and error and sometimes making do with what you have, You need hay though- I buy some of those hay cookies for winter time indoors. Flat discs of hay that they can't cuddle in but they have soft cloths. They DO need to eat hay.
When my boar was neutered we gave him fleece to sleep in and hay packed in loo-roll tubes which kept him busy and meant he couldn't sleep in it (because of his stitches)
Ours go in the run if it's dry but once they get to the stage they don't want to, they'll tell you. Ours sit judgily at the bars glaring as we go by.