To know the angle of why you dreamt of a snake, try going with the way it presented itself, acted or reacted and how you acted, reacted, or interacted with it.

Did you interact with the snake or fear the snake? Is the snake a positive or negative symbol?

In regards to fearing the snake within the dream, fear in general, can be represented in dreams by using an animal you fear in waking life.

In regards to the snake’s behaviour, if it was hissing, maybe it took a strike at you or bit you, then the snake is representing a negative aspect, a danger, maybe a dangerous person or situation.

This is where determining what the snake represents will help determine why you dreamt of it. Maybe you dream of a snake being in your way on your path being, this could allude to your fear being in your way, or a dangerous person or situation is in front of you.

If the snake strikes at you, is this representing yourself striking at another, or maybe the other way around, someone is striking out at you.
If the snake bit you, then the act of biting would contribute to the meaning of what the snake is symbolising. Biting alludes to a negative aspect affecting you in a harmful way, and where the snake bit you will also highlight what that part of the body represents.

If you know the specific snake, then the snake’s behaviour can add to the message of the snake itself, for example, a king cobra is one of the most aggressive and dangerous snakes, it could represent a negative aspect, either yourself, someone else or a situation that is poisonous. Try inserting ‘life-threatening aspect,’ into the message of the dream and see if it fits.
Snakes teach us to shed, you could dream of a snake to symbolise rebirth or transformation. Because they moult their skin as one piece including the skin that forms the eye cap, is there something in your life you could or have let go of completely that also includes your view or perception? So, try inserting ‘renewal or transformation’ into the message for the dream and see if that fits.

There are some collective symbols using the snake that may influence why a snake appeared in your dream:
The serpent and the apple, symbolising your shadow side, or temptation and evil.
The Rod of Asclepius, the symbol of health, Asclepius being the God of medicine.
The ourobus; the circular snake swallowing its own tail, symbolising wholeness, and eternity.
The snake is also associated with the stars and the pattern they move throughout the universe and the kundalini.
These collective meanings are more likely to apply if you have recently learnt such a thing or it is somehow a part of your principles, yet this is not the rule.

The colours or patterns will also help you add more detail to what the snake is representing. If it was green, is this alluding to healing or a brilliant multi-coloured could be alluding to a kundalini transformation.

If you have feelings, thoughts, or associations with the snake, this will most likely be what they are symbolising, if you have no associations, use the scene, stage and setting to use one of these angles.