Question

In this sentence, is summer a noun even though it is a direct object?
Go during the summer.

Answer 1

Yes. Summer is a noun.

Direct objects are always nouns or pronouns.

I think you're confused about the 8 parts of speech (noun, pronoun, adjective, adverb, verb, preposition, conjunction, interjection) and parts of a sentence (subject, verb, direct object, etc.)

Answer 2

http://www.uottawa.ca/academic/arts/writcent/hypergrammar/grammar.html
You can get explanations about the parts of speech (noun, pronoun, etc.) and the parts of sentences (subject, verb, etc.) by using the list at the left.

http://www.chompchomp.com/menu.htm
And here ... in the Terms section.

http://members.cox.net/lenco1/grammarpractice/
And here ...