German nouns are divided into three genders:masculine, feminine and neuter.
The articles are declined depending on what type of gender AND function the nouns have in the sentence.
Mein is a possessive pronoun and is declined just as the indefinite article.
Here we have nominative: for masculine nouns it is for instance Mein Mann, for female nouns it is Meine Frau, for neuter nouns it is Mein Pferd.
There are numerous links on the web, search for "german indefinite article declension"
Darf ich bitte eine Frage stellen? In high school, my German teacher (From Austria) said that if "das" is being used to say "this/that" as opposed to "the", it is to be spelled "dass", note the two "s"'s... Is this the Austrian way of doing things, or has there been a spelling reform, or what???
Don't know about Austrian but I think that in German dass is only used as that in a purely grammatical function. It is a connector.
My English sentence I just used in this post says....I think that in German....
In that sentence that does not refer to anything. It is simply a grammatical concept used to connect the concept of ...I think .... to the rest of sentence ....in German.....
Basically I'm saying that dass is used to represent that only when that doesn't actually mean anything in itself. So your teacher was correct. When using that purely as a connector where it does not actually refer to anything, you use dass.
Otherwise use das.
That (das) is my understanding, that (dass) the difference is as I explained.
In this case Pferd is in the nominative case.
With the various forms of the verb to be. the subject and what looks a bit like the object are actually the same thing. Whatever this ends up being, it is the horse. The sentence tells us that. That means whatever the horse is, it is this. This and the horse are the same thing in this sentence so they are treated the same. That feature also applies to whatever modifies them.
Pferd is subject/nominative even though it is placed where we expect objects to be, so therefore the modifier mein is as well.
If you are interested in the technical terms and grammar rules about this, check out complement and copula on some English grammar pages.
For it to be dative, as you suggest, the sentence would have to say that some action of the verb was being done to, for, at, in, by, with etc. the horse. But in this sentence it is the verb to be. There is no action or event concerning the horse (direct object/accusative) or .....(insert a preposition from the list I mentioned here)... the horse (indirect object/dative).
Some prepositions in German require the accusative case for what follows. Some prepositions require dative. Some take both. The better your understanding of the use of dative/accusative in English, the shorter the lists that you will have to memorize. If you know that with generates the dative in English and you know that mit means with, you won't have to include mit on any memory list because you already understand why mit takes the dative case in German.