According to the Zohar (Beraishis 35b), the snake in the garden was Satan (aka the Yetzer Harah) who is one of the angels. This angel's mission is to be an opposing force to humankind which gives people the ability to choose between following different paths in life. It is brought down that his name is סמא"ל which stands for סיום מסכתא אין לעשות ie is equivalent to the opposition we have in our lives to learning Torah and finding God.
In reference to your question, while angels have Independence and can "do things" on their own, they have no free will in the way that people have free will.
According to the Rambam in hilchos teshuvah, man's free will has two levels, the one relevant to this discussion is the ability to define one's self and direction in life. Angels do not have this ability because an angel and its mission are the same thing (see Bereishis Rabbah 50:2, "One angel cannot have two missions. Neither can two angels share the same mission"). This is why an angel in Hebrew is called 'malach' meaning messenger. The message is its defining characteristic, not its "self". It is a purely spiritual being tied only to its mission (see Rabbi Aryeh Kaplan's translation, "Sefer Yetzirah: The Book of Creation in Theory and Practice" for a more in depth explanation of this concept).