Can you go into the area to cut, and cut the undesirables right now? You could then get a jump-start on the growing season, and have the loggers come in later. I had a forester on the property and she told me to cut when the trees (in particular to me, Aspen) were dormant. She was wrong about a few other things, so maybe she was wrong about this, but that's when I've always cut, and this year I will time my cutting right at, or just before spring thaw so that my cuttings will be available for the deer's return from the yards.
If your deer are around right now, a good cutting may really help them as far as fawning and early antler growth. Also, there will be considerably less damage, especially in wet areas, if you have the logging completed in the winter time.