I came across this simple definition in my lesson, and I was wondering what the difference between these statements is. Both of them have the same meaning, "I wear orange pants". Is it a difference in assignment, or is it negligible?
オレンジ色のズボンを履きます is the right choice. Since オレンジ is a no-adjective, you need to add の to make it modify a noun (ズボン).
Omission of の is allowed only when "オレンジ色ズボン" is presented as an established set phrase. For example, we can say ピンクリボン without の because "Pink Ribbon" is a set phrase. Please see the following related questions.