Hann ríður hestinum.

Because the verb ríða governs the dative when it means to ride an animal or mount.

So even though hestinum is the thing being ridden, Icelandic does not treat it like a normal direct object in the accusative here. This is just something you have to learn with the verb.

• ríða hesti = ride a horse
• ríða hestinum = ride the horse

A very important point for English speakers:
dative does not automatically mean indirect object. In Icelandic, many verbs simply require a certain case.

The base form is hestur, which means horse.

Here is the singular declension with the definite form as well:

• nominative: hestur / hesturinn
• accusative: hest / hestinn
• dative: hesti / hestinum
• genitive: hests / hestsins

In your sentence, the verb ríður requires the dative, so you get hestinum.

Because Icelandic usually puts the definite article onto the end of the noun instead of using a separate word like English the.

So:

• hesti = a horse / horse in the dative
• hestinum = the horse in the dative

The ending -num here includes the definite article in the dative singular form.

Ríður is the 3rd person singular present tense of the verb ríða.

That means it goes with subjects like:

• hann = he
• hún = she
• það = it

So:

• ég ríð = I ride
• þú ríður = you ride
• hann ríður = he rides

This sentence uses hann, so ríður is the correct verb form.

More or less, but a few sounds may be unfamiliar.

A rough English-friendly guide is something like REE-thur, though that is only approximate.

A few details:

• í is a long ee sound
• ð is like the th in this, not the one in thing
• u in -ur is not exactly like English oo; it is a different Icelandic vowel
• Stress in Icelandic is usually on the first syllable, so RÍ-ður

So ríður starts with the stressed rí-.

It can often cover both ideas, depending on context.

Icelandic does not have a separate continuous form like English is riding in the same way. So the simple present can mean things like:

• he rides the horse
• he is riding the horse

Context tells you which one is meant.

If you need to make the ongoing meaning especially clear, Icelandic can use other expressions, but the plain present tense often does the job.

Yes, Icelandic can sometimes leave out the subject less freely than some languages, but in a normal standalone sentence, hann is very natural and clear.

• Hann ríður hestinum. = He rides/is riding the horse.

If you only said Ríður hestinum, it would usually sound incomplete unless the subject is already very clear from context, for example in conversation or in a question/answer exchange.

So for learners, keeping hann is the safest and most natural choice.

Hann is in the nominative case, because it is the subject of the sentence.

In this sentence:

• hann = subject, nominative
• hestinum = object required by the verb, dative

So the sentence shows a very common Icelandic pattern:

nominative subject + verb + dative object

When it means to ride something like a horse, yes, you learn it with the dative.

For example:

• ríða hesti = ride a horse
• ríða hestinum = ride the horse

More generally, Icelandic verbs can have different meanings and different case patterns, so it is best to learn them as combinations:

• ríða + dative

That is a very useful habit in Icelandic, because case government is an important part of vocabulary.

The most neutral word order is:

• Hann ríður hestinum.

That is the standard subject + verb + object/complement pattern.

You can move parts around in Icelandic, but that usually changes the emphasis or sounds more literary, poetic, or marked.

For example, putting hestinum first would emphasize the horse in some way. For a basic learner sentence, Hann ríður hestinum is the normal order to use.

Hestur is a masculine strong noun.

That matters because Icelandic noun endings depend on:

• gender
• number
• case
• definiteness

So if you learn that hestur is masculine and strong, it becomes easier to understand forms like:

• hestur
• hest
• hesti
• hests
• hesturinn
• hestinn
• hestinum

This is one reason Icelandic learners are usually encouraged to memorize nouns together with gender and, ideally, a few key forms.

You would remove the definite article ending, so:

• Hann ríður hesti.

Compare:

• Hann ríður hesti. = He rides a horse.
• Hann ríður hestinum. = He rides the horse.

The case stays dative because the verb ríða still requires it. Only definiteness changes.

Because it is made up of meaningful grammatical pieces.

In hestinum, the ending tells you important information:

• it is singular
• it is dative
• it is definite (the horse)

So Icelandic endings often pack several meanings into one form. That is why a single word like hestinum carries much more grammar than the English word horse.

For learners, it helps to think of Icelandic noun endings as signals rather than random changes.