Hay isn't appropriate bedding -- it's not very absorbent. They do need it all the time 24/7 as much as they can eat for their dental health, however. People use aspen shavings, Carefresh, and other small animal beddings for the cage itself.
Like Sasami said, your house is plenty warm for them and if theyre outside maybe they can be brought in so they're not in the miserable cold.
We are as gods to the beasts of the fields. We order the time o' their birth and the time o' their death. Between times, we ha' a duty. - Terry Pratchett.
"Men have forgotten this truth", said the fox, "But you must not forget it. You become responsible, forever, for what you have tamed. - Antoine de Saint-Exupéry