'except' is a preposition, and pronouns with a preposition take the objective case, just like:
with him
between you and me.
So the sentence is:
"All the students except me are going for a walk."
'except me' is part of the subject; but if the subject of a sentence contains a preposition + pronoun, the pronoun is in the objective case, not the nominative.
You will find a list of all the prepositions - and some may surprise you! - at:
