The trees do not seem to be of any specific type of discernible species. Their upper boughs are never seen, so it is unknown if they possess any kind of foliage. They do appear to be twisted with vines that are as white as the trees themselves, hinting that they may be part of the trees.
On their way home from school Abbie and Jenny Mills both saw Moloch raising Jeremy Crane aka War from his grave. Both girls fainted and the details of that day were hidden from them, so they could not accurately remember the features of Jeremy, and thus did not recognize him when they later met him as Henry Parrish.
This event was the beginning of the girls' downward spiral in life. Abbie denied the experience and said she merely fainted while Jenny stated the truth until she was deemed insane, and was later institutionalized. It was here that she faced repeated possession by a demon. Both girls were later met by Sheriff August Corbin, who helped give both girls direction in life. In the case of Abbie, she was inspired to become a police officer, while Jenny was freed of possession by Corbin, and later aided him by tracking down artifacts of importance.
Whether the trees possess power of their own, or are merely totemic representations of the the Four Horsemen is unknown. It is evident that they can appear and disappear for unknown reasons, and that the dark being connected with them -such as Jeremy- can control them in some way, such as using the vines that cover the trees to restrain people, like his parents Ichabod and Katrina Crane.