"You have horses."
Translation:Du hast Pferde.
It's wrong because the pronoun and verb form don't match (singular informal pronoun with plural informal noun). It sounds wrong in the same way that "you has horses" does, as an analogy.
singular informal: du hast
plural informal: ihr habt
formal (either singular or plural): Sie haben
Were these cases adopted after contact between early Germans and the Roman Empire? If so, what happened to the ablative case? (Faint memories of school Latin still linger!) Also are all these cases for the plural (Pferde) - as my dictionary seems to give a different ending for the genitive of the singular (Pferd) as -(e)s !
Were these cases adopted after contact between early Germans and the Roman Empire?
No -- the concept of cases was inherited from Proto-Germanic, which inherited them from Proto-Indo-European (PIE): the same place that Latin (and Sanskrit, and Greek, and Slavic languages, and ...) got their cases from.
Proto-Indo-European probably had eight cases, maybe nine ( https://en.wikipedia.org/wiki/Proto-Indo-European_language#Noun ).
Proto-Italic (between PIE and Latin) still have seven of them ( https://en.wikipedia.org/wiki/Proto-Italic_language#Nouns ; including a separate locative case -- but no instrumental case any more). Even Old Latin had preserved the locative case ( https://en.wikipedia.org/wiki/Old_Latin#Nouns ), but in Classical Latin, the locative case was essentially dead (partly due to sound changes: see https://en.wikipedia.org/wiki/Locative_case#Latin ), leaving only six cases ( https://en.wikipedia.org/wiki/Latin_grammar#Case ).
In Proto-Germanic (PGmc), on the other hand, six of PIE's eight (or so) cases were preserved ( https://en.wikipedia.org/wiki/Proto-Germanic_grammar#Nouns ): nominative, genitive, dative, accusative, vocative, and instrumental. A set similar to that of Classical Latin, but with an instrumental rather than an ablative. I'm not sure what happened to the ablative or locative cases on the way from PIE to PGmc.
Proto-West-Germanic (the ancestor of English and German, but not, say, Danish or Gothic) still had those six cases ( https://en.wikipedia.org/wiki/West_Germanic_languages#Nouns ).
Old High German had lost the vocative, giving five cases: nominative, genitive, dative, accusative, and instrumental ( https://en.wikipedia.org/wiki/Old_High_German_declension#Grammatical_cases ).
By the time of Middle High German, the instrumental had also disappeared ( https://en.wikipedia.org/wiki/Middle_High_German#Nouns ), giving the four-case system that has survived all the way to Modern High German.
If so, what happened to the ablative case?
You might as well ask what happened to the instrumental case in Latin :)
Also are all these cases for the plural (Pferde)
Yes: the four case forms I quoted in my answer were for the plural.
Thank you very much for your detailed answer, mizinamo! At a first glance at these links, most languages seem to have simplified the number of noun cases (perhaps with the exception of Russian) from those of the PIE, but great importance still attaches to the slightly different endings of words in the languages I have come across, even if not on your PIE chart, like Finnish and Hungarian.
How would I know if it was du hast or Ihr haben?
Because you've hopefully been reading the tips and notes for each new lesson unit before starting it.
They're available on the website by clicking on the "tips" or "lightbulb" button after selecting a lesson unit:
And so you read in the "Accusative Case" unit notes ( https://www.duolingo.com/skill/de/Accusative-Case/tips-and-notes ) that du hast is correct but ihr haben is wrong; it would have to be ihr habt. Just like pretty much all ihr verb forms end in -t.
Now -- whether to translate "you have" into du hast or ihr habt is not something you can predict: and therefore both of those translations are accepted.