For you, you did the wise thing. Otherwise you would not have gotten a good night's sleep. I believe that for many reasons some people are just afraid of some things. By the time we become adults it is hard-wired to our psyche. And often there is nothing we can do about it.
I have no experience with copperheads, so I cannot comment on their behavior. However I do have a lot of experience with rattlesnakes in California. By experience, I mean I have seen many of them. I don't bother them, and they don't bother me. These snakes are more afraid of us, than we are of them.
I have a theory about rattlesnakes found around fairly well used trails. They rarely rattle, at least not in the past 20 years or so in my experience. I think it is because those that rattle are killed, and those that do not survive. We have probably influenced selective reproduction. The none rattlers live, we kill the rest. When I travel cross country, I hear them rattle, often from quite a distance.
The snake below did not rattle, and I almost stepped on it, not seeing it, as I was looking down canyon at the view. My wife saw it, freaked out, and refused to continue until I moved it. A couple hours later I almost stepped on it again, as it had returned to the same spot. :)
This one was pretty big. No rattling either.