Take it one step at a time.
Don't worry about the add to cart yet. That will be the easy part.
You will be filtering from the results of a form post. All your checkboxes should be within a single form with a single submit button (later to act as the add to cart button, but like I said don't worry about that yet).
I don't think you need cookies or sessions to create your filter it can all be done from the form.