Mér er kalt, þess vegna drekk ég heitt te.

Because this is a very common Icelandic way to express a physical feeling or state. Literally, Mér er kalt is close to To me it is cold.

For sensations like being cold, hot, in pain, etc., Icelandic often uses:

• a pronoun in the dative case: mér = to me
• the verb vera: er
• an adjective in neuter singular: kalt

This is the normal way to say I feel cold.

Mér is the dative singular form of ég.

Icelandic uses the dative in a number of expressions for feelings and bodily states, especially with words like:

• kalt = cold
• heitt = hot
• illt = painful / bad
• leið = bored

So mér er kalt follows a common pattern where the experiencer is in the dative rather than the nominative.

In this kind of expression, the adjective normally appears in the neuter singular form, which here is kalt.

So:

• Mér er kalt = I feel cold
• Mér er heitt = I feel hot
• Mér er illt = I am in pain / it hurts

This is different from sentences where the adjective describes the person directly and agrees with their gender:

• Ég er kaldur = I am cold / cold to the touch / cold in manner (male speaker)
• Ég er köld = same idea (female speaker)

For the temporary feeling of being cold, mér er kalt is the usual expression.

Not a normal nominative subject like ég.

Learner grammars usually treat this as an impersonal construction: the verb stays in the default 3rd person singular form, er, and the experiencer appears in the dative as mér.

So even though mér refers to the person feeling cold, the structure is not the same as a regular Ég er ... sentence.

Because Icelandic main clauses usually follow the V2 rule: the finite verb comes in the second position.

Here, þess vegna takes the first position, so the verb drekk must come next, and the subject ég comes after it.

Compare:

• Ég drekk heitt te.
• Þess vegna drekk ég heitt te.

This verb-second word order is one of the most important patterns in Icelandic.

Þess vegna means therefore, for that reason, or that is why.

It links the second clause to the first:

• Mér er kalt → that is the reason
• þess vegna drekk ég heitt te → that is the result

For learners, it is best to treat þess vegna as a fixed expression.

They are related in meaning, but they work differently:

• þess vegna = therefore / that is why
  It introduces the result.
• vegna þess að = because
  It introduces the reason.

Compare:

• Mér er kalt, þess vegna drekk ég heitt te.
  I am cold, therefore I drink hot tea.
• Ég drekk heitt te vegna þess að mér er kalt.
  I drink hot tea because I am cold.

So they express the same logic from opposite directions.

Because the subject is ég, and drekk is the 1st person singular present form of drekka.

Present tense:

• ég drekk = I drink
• þú drekkur = you drink
• hann / hún / það drekkur = he / she / it drinks

So drekkur would not fit with ég.

Because adjectives in Icelandic must agree with the noun in:

• gender
• number
• case

Here:

• te is a neuter singular noun
• it is the direct object of drekka, so it is in the accusative
• with no article, the adjective takes the appropriate strong form

That gives:

• heitt te

So heitt matches te grammatically.

No. In this sentence, te stays te.

That is because te looks the same in the nominative and accusative singular. Even though it is the object of drekka, its form does not visibly change here.

So the case is shown more clearly by the adjective heitt than by the noun itself.

Yes. The sentence contains two main clauses:

• Mér er kalt
• þess vegna drekk ég heitt te

A comma between them is normal written punctuation. You could also split them into two sentences in some contexts, but the comma is perfectly natural here.