The answer is true.
An adverb clause contains a subject and a verb and functions as an adverb , so it modifies a verb, adjective or adverb.
In the example sentence, the adverb clause expresses cause and effect: "because the rain ruined the grounds." The statement does not need a comma after postponed because the adverb clause is at the end of the sentence, so the coordinating conjunction because indicates separation between the two clauses.
