У лошади болит копыто.

Because Russian often uses the pattern у + genitive + болит/болят + body part for aches and pains.

So the structure is:

• у лошади = of the horse / by the horse
• болит копыто = the hoof hurts

Literally, it is something like At the horse, a hoof hurts, but natural English is The horse's hoof hurts or The horse has a sore hoof.

This is a very common Russian pattern:

• У меня болит голова = My head hurts
• У собаки болит лапа = The dog's paw hurts

After the preposition у, Russian uses the genitive case.
The noun лошадь changes to лошади in the genitive singular.

So:

• dictionary form: лошадь
• after у: у лошади

This is just normal case change, not a special idiom limited to this sentence.

By itself, лошади can be ambiguous, because it can be:

• genitive singular of лошадь
• or nominative/accusative plural

But after у, it must be genitive, so here it means of the horse, not horses.

If you wanted of the horses, you would say у лошадей.

In this Russian construction, the body part that hurts is the grammatical subject.

So in:

• У лошади болит копыто

the subject is копыто.

That is why the verb agrees with копыто, not with лошади.

English works differently: we often make the possessor sound more central, as in The horse's hoof hurts. Russian makes hoof the grammatical subject.

Good question, because for an inanimate neuter noun like копыто, the nominative and accusative forms look the same.

So the form alone does not tell you. What tells you is the sentence structure:

• болит is an intransitive-style predicate here
• the thing that hurts is the subject
• therefore копыто is nominative

Also, the verb болит is singular, agreeing with копыто as subject.

Because копыто is singular.

Russian present-tense verbs agree with the subject in number, and here the subject is копыто.

• копыто = singular → болит
• копыта = plural → болят

So:

• У лошади болит копыто = The horse's hoof hurts
• У лошади болят копыта = The horse's hooves hurt

Because лошадь is not the grammatical subject here.

It matters that лошадь is feminine for forms like:

• лошадь
• у лошади

But the verb does not agree with it in this sentence, because the subject is копыто, which is neuter singular.

So the agreement is with копыто, not with лошадь.

Yes. Russian word order is flexible because case endings show what each word is doing.

The most neutral version is:

• У лошади болит копыто.

You may also hear:

• Копыто у лошади болит.
  This puts more emphasis on копыто.

• У лошади копыто болит.
  Also possible, a bit more conversational in feel.

But for a learner, the original order is the safest and most standard.

Russian has no articles, so there is no direct equivalent of the or a.

Also, Russian often does not use a possessive word like its or the horse’s when possession is already clear from the structure.

In У лошади болит копыто, it is already obvious that the hoof belongs to the horse, so Russian does not need an extra possessive word.

Depending on context, English could translate this as:

• The horse's hoof hurts
• A horse has a sore hoof
• Its hoof hurts

Yes, but it means something slightly different.

• У лошади болит копыто = specifically the horse’s hoof hurts
• Лошади больно = the horse is in pain / it hurts the horse

So больно gives a more general idea of pain, while болит копыто names the exact body part.

The stress is:

• У лоша́ди боли́т копы́то.

So:

• лоша́ди → stress on а
• боли́т → stress on и
• копы́то → stress on ы

Stress matters in Russian, so it is worth learning these together with the words.