Trees, especially large and old ones, are said to be rich in prana or chi.
In eastern medical systems, prana or chi/ki is said to bring about healing. When there is prana blockages or low prana in the human system, disease is said to arise. Ayurveda, acupuncture, reiki , pranic healing , pranayama in yoga all deals with prana.
So sitting under large trees is recommended for diseased people in eastern medical systems so that they can gain the prana from the trees next to them.
I would say hugging trees in love is thus a natural sentiment because you know instinctively or intuitively that you are gaining healing energy in the process.
Your post is inspiring and reminds me to do my own charging up by sitting under some good old trees or hugging them as well.