Is cut up yarn or string inside pillowcases okay to put in the cat house?

Materials made of fabric will retain moisture and freeze, pulling heat away from the cat and making them colder. It is also likely to mold if some moisture gets in. Straw (not hay) and shredded newspaper would be cheaper than yarn/string, and allow the cat to burrow into it. String and yarn can be dangerous. If the cat gets into the pillowcase while trying to burrow and swallows some, it can kill them by getting twisted in their intestines. Newspaper will also hold water if moisture gets in, but is a second-best alternative to straw if you check it regularly after snow/rain.