D, I'd need to know where you live and how cold/wet it gets before I could
answer your question completely. Plus, how old are your logs?, have they fruited yet?, what kind of shape is the
wood in?
But basically, if someone lived in zone 2 or 3 (very cold) or where the ground freezes solid for months at a time, I would suggest bringing the logs in, especially if they haven't fruited yet. But it's crucial that they don't dry out either, cause once they dry out too much, they might not fruit at all. But old logs in danger of losing their bark layer might benefit from protection from snow/ice/nonstop rain as well. I live in the Pacific Northwest (zone 8 ), and I'm leaving my oyster logs and chip boxes outside this year, with just a thin plastic cover over them sometimes. I started the logs inside late last winter and kept them inside a bunch of plastic bags in the closet while they were on their spawn run. They were covered with mycelium when I put them outside in June.