Given that the series draws so heavily from Native American mythology, and given what I know as a social worker serving Indigenous communities in Canada.
It seems that Lynch is borrowing the owl motif from the original peoples of Turtle Island (North America). Many First Nations (Native) groups regard Owls as a symbol of death and a bad omen. You will remember seeing many Haida style totems of Owls in Ben Horne's office and other rooms at The Great Northern.
Native American symbols are geometric portrayals of celestial bodies, natural phenomena and animal designs. Native American bird and animal symbols and totems are believed to represent the physical form of a spirit helper and guide. The meaning of the Owl symbol signifies a bad omen.
From this source
According to Native American legends and myths of some tribes the Owl is a symbol of death. The owl is a creature of the night and was strongly associated with the supernatural. The circles around the eyes of an owl are believed to be made up of the fingernails of ghosts. Owls were also believed to be messengers from beyond the grave and would deliver warnings to people who had BROKEN TRIBAL TABOOS [relevant to the incest themes of TWIN PEAKS]. Even to hear an owl hooting was considered to be an unlucky omen. The Pueblo people, including the Hopi tribe, associated owls with their belief in witches [Dugpa's & Lodge Sorcery?] and the feathers of owls have a very sinister significance. For additional information refer to Power Animals.
(emphasis and parenthesis mine)
By all this I mean to add credence to the theory which states that the significance of Owls in the series is indeed a connection to the occultism of the Black Lodge and the malevolent spirits therein, as well as the way in which these entities are a reflection of the dark side of the townsfolk (Leland and Ben chiefly especially in exploiting their daughters, but most others in some sense also).
In the spirit of psychoanalytic interpretation of Lynch's cannon I wish also to state that an ethnopsychiatric perspective on the Owl mythology would suggest that they are a representation of what Freud called the 'Death Drive' or Thanatos in opposition to Eros or Love. Remember that the the keys to the white and black lodges are love [empathy] and fear [annihilation anxiety] respectively I wonder if Lynch has read Melanie Klein's work on the Good and Bad object (read: breast; peaks?) as much of his work seems to deal with schizoid defences such as splitting (the sorting of experience into polar categories of good vs evil, nurturance and pleasure vs neglect, anxiety and frustration).