When your pig lives outdoors, you need a different type of bedding. You should have straw and shavings. Pine shavings are the best shavings to use in their outdoor space. Also housing should be wood, not plastic, whenever possible. Especially if it's an outside pig that lives outdoors all the time. That's very important because the wood breathes and it's cooler in the summer, and warmer in the winter for you. Then, the housing should be double-walled or at least insulated so that it keeps them warmer inside. You can use straw or you could use hay as well. They may like hay because they can eat a little of it as well, and it gives them a little more roughage if they're outside pigs. But the straw is a better bedding than the hay is.
Your outside house really should have a doorway that's adequate for the pig to come and go, but not too big so that it doesn't create a lot more draft in the wintertime. It should also have a flap on it. The flap should be waterproof so that no water is getting in, and the flap will keep the inside of the house warmer as well.
I don't recommend that you use blankets in an outdoor facility, mainly because the pig will use that blanket to block the doorway and then the rain will come or snow. It will become moist and then we don't want moisture inside of their little contained areas.