Thinking about this afterwards, I'm wondering whether the noise of a barking dog I had heard when I first got out of my car was a signal from a sentry creature up in a tree which either saw me or heard me close my car door. The first sharp noise (which I ignored and kept on hiking) could have been an alarm when I crossed into an area being defended and the second sharp noise could have signalled me leaving the area.
The absence of any deer, birds or even small animals throughout my hike should have also been a clue at the time. Usually when I hike in the woods during a light rain I get to see a lot more wildlife. (One time I witnessed a rabbit playfully jumping back and forth over a water puddle-- I wouldn't have believed it if I hadn't seen it for myself.)
I now realize that the increased visibility in the woods works both ways. Whereas I thought it gave me an advantage of seeing a longer distance into the brush, likewise these creatures could keep track of where I was and stayed out of sight. I should have anticipated that they would have taken up temporary residence in the woods on public property while hunters were prowling around the private hunting club. They were probably keeping an eye on me the whole time.