I will also say that in English, we have the words "does", "do", and "did", which most other languages do not as identifiers. So, in consideration of this in the sentences, translating "Ele tem un cavalo?" to English would require us to put "DOES he have a horse?"... that being said Duolingo should still accept both formats of response.
He has a horse? is perfectly correct, but the question mark is required. Duolingo does not care about quotation marks when scoring answers. In spoken English you would hear that the sentence has a different intonation difference. And if you were to read it aloud the question mark would tell you to read it as a question.
You are of course right that people speak the way they want and thereby create the grammar of the language. This, however, also goes for the meaning of words, as poets show us through their work. This flexibility even goes for the word enforce as used in the commentary above where the authors seems to use it in the meaning of "want you to apply a certain grammatical form by not approving the alternative".
The 'm' in "tem" shouldn't be pronounced. When 'e' is followed by 'm' (or 'n') it is nasalised and "tem" should sound more like "teng" (though that hardly does the sound justice). If you are familiar with the international phonetic alphabet, this dictionary shows the correct pronunciation: http://en.wiktionary.org/wiki/tem. Or you can hear it spoken by native speakers: http://www.forvo.com/word/tem/#pt.