Shiitake is very used to freezing temperatures. -1 is pretty cold. They can have a setback if it's too cold before they really are inoculated, but they still generally work. Most people in cold climates like yours inoculate after March 1st, when it might freeze, but it won't get really cold. On the other hand, if you keep your logs on a pallet and away from the soil, there probably won't be a lot of other growth happening on them til later. Some have wrapped them or brought the logs into a garage or basement, so it won't be so cold as well. You have several options, all of which
should work. You are very lucky to have oak logs, something most mushroom cultivators would love to have.
John S
PDX OR