"나는 장갑을 끼고 학교에 갑니다."
Translation:I go to school wearing gloves.
Your sentence is semantically correct (It preserves the general idea of the sentence) but syntactically (grammatically) inaccurate as it does not express the relation between two clauses* which in the given example is represented by the coordination conjunction "고, and".
(* clause is a kind of mini sentence which should include a verb)
"on the way to school" as you have suggested is only a phrasal adverb (of location), not a clause.