The ideal time to cut logs is late winter for early spring inoculation. This maximizes time for the mycelium to grow into the log before the winter freeze. However, you can inoculate throughout the year, and it is generally best to plug your log within 2-4 weeks of the tree falling.  Fall is an awkward time, and you need to make a call whether to inoculate now or let the logs sit through winter and inoculate early spring.  If the weather in your location is already below zero, there would be no harm to let the logs sit through winter, as there is little chance of wild fungal competitors invading your log during this time. If you did choose to inoculate, your mushroom mycelium won’t have much opportunity to grow from the plugs into the logs either, and may be compromised by extreme cold. If you anticipate a month or more of above zero daytime temperatures, or you can place your logs in a basement or greenhouse that will be warmer than outside, then there would be an advantage to inoculating immediately and giving the logs a head start.