C S Lewis claimed trees could stand. The Bible mentions something about having deep roots. Revelation claims even the islands and mountains cannot stand, because they both can be moved. It seems to me only beings have the will to stand in awe, even angels. Now that a third have turned against God, even they are still commanded to stand in awe, until they are released from doing so.
I doubt animals are beings, but some may be classified as intelligent. Do any show fear? Some may be smart enough not to get into a position where they have to run away and hide. Even humans are not that bright when it comes to wild animals that could do great harm to them. There may be a healthy fear. Or perhaps because of sin, humans may not be welcome in some areas of nature, they could probably stay out of.
Standing in awe, or fear seems like a conscious choice of beings who can reason and understand the ability to do so.