"On Horse Market"
"On the Horse Market"
I suspect the latter is correct, but I do not know why? I did some research. I know that market is countable. Is that a rule that I always have to put an article before countable nouns?
Although horse markets are rare in the modern world, there are other types of market, e.g., the stock market or the bond market. The word "market" takes an article because it is a countable noun.
I bought this horse at a horse market
The speaker does not think the specific location is relevant.
I bought this horse at the horse market last year
implies a specific market for horses that is presumably understood by both speaker and audience.
Is that a rule that I always have to put an article before countable nouns
When the noun is not a proper noun, and referring to something that, in that sentence, can be counted, then yes.
If you can answer the question which X sensibly, then X is countable.
On Horse Market
Proper nouns in English are capitalized. You don't use an article here because of that.
Horse Market also happens to be composed of words that also work as non-proper nouns. When used in a non-name sense, the normal article rules would apply.
I went to the horse market that's down the street.
I went to Horse Market yesterday.
I talked to that guy yesterday.
I talked to John yesterday.