To many people, their nightly dreams mean nothing more than a way to entertain others around the breakfast table. But psychologists, most notably Drs. Sigmund Freud and Carl Jung, have done an enormous amount of work based on the idea that dreams have meaning and that attempting to understand our dreams can be helpful.
The idea that dreams have meaning presumes an unconscious level of our minds from which dreams come. Dreams, such as your dramatic dream of the green snake, can contain vivid symbols that seem to have little to do with our normal waking world. It could be that you recently went to the zoo and saw a snake, and the dream was merely reflecting that waking experience. However, even when our dreams seem to replicate the events in our outer lives, there is usually something different, such as the snake's chasing you (which Doctor George assumes did not happen at the zoo).
The particular meaning of the snake in your dream would depend on your associations to it and on what intuitively "clicks" for you as you consider various possibilities.
It may be literal, so we might first look at your personal experiences with snakes to see if there is some unresolved issue or fear there. You could think about the particulars of the dream, such as the snake's skin and eye color, and see if these mean anything to you.
It may be spiritually symbolic. In the Bible, the serpent, in the Garden of Eden, has traditionally been portrayed as the cause of Adam and Eve's downfall. However, their gaining the "knowing of good and evil" could also be interpreted as the beginning of humans becoming conscious.
We could look deeper into the symbolism of the snake as it appears in history, myth, legend and religion. For example, in Hinduism's concept of the body's Chakras or energy centers, yellow is the color of the third Chakra located in the solar plexus, a power center of the body that is believed to relate to a person's identity and willpower. In ancient times, the Greek god of healing Asklepios carried a staff with a snake winding around it. People went to temples of Asklepios so they could sleep on a stone bed (called a cline, from which our word "clinic" is derived) and have a dream. The dream of being bitten by a snake was seen as a sign that you would be healed of whatever malady you had. The snake also appears as a symbol of feminine spirituality and power in a Minoan sculpture of a bare-breasted goddess with a snake wrapped around each arm.
It may be metaphorically symbolic. In general, the snake may be seen as a symbol of the renewal or rebirth of one's life because, as it grows, it sloughs off its old skin. The color green, the color of vegetation goes along with the idea of new life. Osiris, the Egyptian god of renewal and rebirth, had green skin.
It may be a message about your feeling constricted and having a need to shed a constricting behavior, situation, or person from your life. That would also be consistent with the theme of a snake shedding its skin.
It may relate to your age. As someone in their thirties, you're at a transition point: no longer in your twenties but not yet middle-age. A saying, in the '60s, was "Don't trust anyone over 30." That signified the beginning of the demarcation between younger and older adults. So, the snake may represent your need to become aware of your new age status.
It may represent some problem or area in your life that you have tried to avoid but just won't go away. Like the problem, the snake won't let you shake it; it tracks you down. And, the more you try to avoid it, the more hostile it becomes. You might want to think over what parts of your life feel similar: that is, what feels like a problem to avoid yet, if faced, would lead to your personal growth.
P.S. An excellent book on dream interpretation is John A. Sanford's Dreams and Healing. Scientific studies on sleep and dreams can be found in Wm. C. Dement's Some Must Watch While Some Must Sleep.