The infinitive phrase is "to spend the afternoon tobogganing".
An infinitive phrase expresses the action in a sentence. They can often function as nouns, adjectives or adverbs. E.g.: To win the approval of her mother-in-law by cooking dinner was Mary's only hope. The infinitive phrase in bold functions as a noun because is the subject of the sentence. When the phrase explains 'how' it functions as and adjective, when the phrase explains 'why' it functions as an adverb.
