I've noticed this as well. Just the thought of being alone in a quiet forest with the sounds of the leaves rustling and the birds chirping, and the smell of the conifers puts me in a relaxed state of mind. I've noticed also that my mind almost reflexively anthropomorphizes the organisms around me, and I have a nebulous hypothesis as to why this is.

Consider this: those who become blind later in life often experience visual hallucinations (Charles Bonnet syndrome). It seems like there is something like a vision module in the brain which, when under-stimulated, starts producing its own content.

Maybe we have a social module as well, which, when under-stimulated by social interaction, starts hallucinating that non-human objects and organisms have human sentiments, and we feel a sense of affiliation as we might toward a human. The happy difference is that there is never a risk of negative social feedback from trees, rocks, or chipmunks, in the same way that there is a low risk of negative social feedback from very young children or kindly old ladies, toward whom I at least also tend to feel a reflexive sense of affiliation.

Thus, the feeling of togetherness we experience in nature is a result of our hallucinating social agents that never give us negative social feedback.

Moreover, exercise and the outdoors make you feel energetic and refreshed for other reasons, and when you feel good, the threshold stimulus for affiliative feeling is certainly lower.