This is belief and experience based(with a little family teaching mixed in). Normally I would not share something like this with just anyone. I do believe some may enjoy it though. I will discuss how I see it, and then share my story of how I came to believe this with you.
In magic, willows are know for their properties of protection, healing, and love. You can burn the bark or wood for spells and cleansings. The bark contains the natural form of asprin (salicilic acid). It is said to be the tree of dreaming. I have found that burning the wood made into incense with lavender helps promote good dreams and peaceful sleep. It can also induce sleep astral projection. Their scientific name (Salix) in Celtic means near (sal) water (lis). They prefer moist ground with a constant water source. Celts believe that willows are powerful psychic forces that can induce visions. They also believed humans to be decendants of trees. They honored them as sacred and a connection to the divine. But enough about others beliefs.
I believe that all trees have a spirit. Each one is unique in its attributes. When you take from a tree you should thank it for its gift/sacrifice. They can live to be thousands of years old. In my family, we believed them to be the spirits of guardians. When a pledged guardian or parent dies, they would be reborn as a tree to keep watch over their pledge or their bloodline. The guardians of my family are mostly reborn as willows (according to my aunt).
Ever since I was a little girl I used to dream of a large white willow. I would climb up in it and lay in its branches. I would sing to it, pray to it, and sleep in it, in my dreams. When I was about six or seven, my parents had to move. We left town to go to out in the country. When we arrived at the property I saw it. The willow of my dreams standing tall in the center of the property. It towered over me, the most gorgeous thing I have ever seen. After that I spent hours every day with my willow. It did not matter what the temperature was, I would be there with it. Every time I was upset, I would dream of my willow.
Often times my dragon guardian would surround me and it. I thought perhaps that is where the dragon lived in spirit. When I was fifteen, I was warned by my dragon guardian while walking around town. It was trying to herd me back to my house by blocking my path. I was badly beaten by some "friends" after ignoring the warning. When I made it home from the hospital, the tree had been struck by lightning. I cried for weeks as my mum had it cut down. I thought for sure that the tree would be gone forever, and my dragon guardian with it. I prayed every day at the edge of the crescent it made, that they would come back for me.
A month later the tree pieces were still in the yard. I went to pick them up for my mum and noticed they were hard to move. I lifted the edge of one of the logs and noticed that roots were growing out from under it. The dragon reappeared to me that night. I later found out from my dragon that they are one. Uriel (my dragon guardian) said that the spirit of the tree is part of him. He said that the guardians plant a tree nere the ones they must watch over. If the guardian dies, the tree dies with it. He said that you must love your tree and take care of it for it is family.
Because of my family teachings, and my experience, I will forever believe in the spirits of trees. Often times I will feel one smiling down on me as I walk past. Sometimes it feels as though one is hugging me when I lean against it. Regardless of what anyone tells me, I will forever care for my tree and the guardian spirit it belongs to.