I get from the article and other sources 2 things:
Wood harvested during the waning cycle of the moon has a higher density than wood harvested during the waxing cycle.
Trees have some biological response to moon cycles, and chemical properties change according to them. This explains how specific timing of cutting can have permanent effects on wood properties.
I also gather this:
Cut wood during the waning cycle if you want to use it to make something, it will be stronger, denser, resonate better (for instruments) etc. depending on the day.
Cut wood during the waxing cycle if you want to burn it. Wood cut during this cycle seems to store more energy, and therefore burn hotter despite the reduced density.
I suspect that the reason for cutting wood in winter cycles may be merely to stave off insect and fungus attacks. It is entirely possible that the moon cycle trends are true year round. I say this, because tropical societies also harvest building materials according to moon cycles, yet have no winter. Tropical climates are divided into dry season and wet season, rather than summer and winter.
Perhaps there is some organization out there that could study this phenomenon in detail among American tree species, and across various seasons and lunar cycles? If true, it would certainly be something for us to take into consideration.
It is said that to this day in Austria, many foresters will stamp logs with the moon cycle and zodiac sign they were cut under. I also read that in centuries past, Violin and cello makers would supervise the cutting of trees to make sure they were cut under the right moon, because that would affect the resonance properties.