No. Polish verbs of motion, like in other Slavic languages, distinguishes between determinate and indeterminate verbs.

What that means is that chodzi refers to frequent trips and movement in general. Idzie on the other hand, refers to a a single trip going somewhere specific.

Verbs of motion are one of the bigger points of trouble for native speakers of Germanic and Romance languages, so I'd suggest Googling "Polish verbs of motion" to find out more. This site has a pretty good explanation, but it's gonna take a while to get used to: http://www.polish-dictionary.com/polish-motion-verbs

In different contexts The horse is walking/ The horse goes.

could be correct.

chodzi = has ability to walk / is walking/walks aimlessly/ goes/walks (somewhere) regularly

This particular short sentence seems to me as is walking aimlessly or has ability to walk

It's just different conjugation class. Its infinitive forms are „chodzić” and „iść”.

"Ten koń chodzi" would mean "This horse is walking," as "ten" is a demonstrative, not a simple definite article. There are no articles in most Slavic languages, so no difference between "a horse," "the horse," and simply "horse."

OK, if it's such a vague sentence as this one we will accept "spaceruje".

It is an accepted answer, it should have worked.

Remember, though, that normally "chodzić" only translates to Present Simple (to go, to walk). It's only because this sentence is so vague, there's no direction nor destination, that 'is walking' may be accepted. If it was "Koń chodzi do sklepu", it could only be "[The/A] horse [goes/walks] to [a/the] [store/shop]". Not "is walking".

Colloquially some people call it „koń”, but the proper term is „skoczek” (lit. "jumper"). And you wouldn't say „chodzi” (because it has no legs), but rather „porusza się”. So in short: „Skoczek porusza się po literze L”.

"Horse walks" is not grammatically correct. It requires either "a" or "the" before it. Even though articles don't exist in Polish, you need to add them when you translate into English.