A coat is read as protection from the cold of the world — the layer you put between yourself and hard weather. Taking it off is traditionally seen as trust, or as feeling safe enough to open up.
Has this come up in your dreams before? What was going on in your life then?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.