If students wore black sweatshirts to protest a war, what sort of free speech would they be exercising

I believe they would be exercising symbolic speech

symbolic speech refers to the type of statement that being conveyed through a certain actions rather than using words.

Even though this type of speech does not directly mentioned in the constitution, it's still considered to be protected under the first amendment.

I believe it would be freedom of expression and freedom of speech. You have the right to protest and express yourself freely within reason. As long as it does not cause another harm it is a moral judgement and should not be held against a person.