Jag vill ha ett glas kallt vatten nu, men hon vill hellre dricka te i en mugg.

In Swedish, vilja means to want, but it is often followed by another verb to complete the idea.

• Jag vill ha ... = I want to have / I want ...
• Jag vill dricka ... = I want to drink ...

So Jag vill ha ett glas kallt vatten is a very natural way to say I want a glass of cold water.

Using ha here is extremely common when asking for food, drinks, or objects.

Because Swedish nouns belong to two grammatical genders:

• en-words
• ett-words

So:

• ett glas = a glass
• en mugg = a mug

You usually have to learn the article together with the noun:

• ett glas
• en mugg
• ett vatten is not used, because vatten is usually an uncountable noun here

This is one of the most important habits in Swedish: learn the noun and its article together.

Because the adjective must agree with the noun it describes.

Here, vatten is an ett-word, so the adjective takes -t in the singular indefinite form:

• kall = common base form
• kallt = used with an ett-word
• kalla = plural or definite forms in many cases

So:

• ett kallt vatten would be grammatical in structure, though not the usual phrase
• kallt vatten = cold water

In the full phrase ett glas kallt vatten, the adjective kallt describes vatten, not glas.

It describes vatten.

The phrase means:

• ett glas = a glass
• kallt vatten = cold water

So the structure is really:

• a glass [of] cold water

That is why the adjective matches vatten and becomes kallt, not something matching glas.

Swedish often leaves out of in this kind of expression.

English:

• a glass of water
• a cup of tea

Swedish:

• ett glas vatten
• en kopp te

So ett glas kallt vatten literally looks like a glass cold water, but it means a glass of cold water.

This is completely normal in Swedish.

Hellre means rather.

In this sentence:

• hon vill hellre dricka te = she would rather drink tea

With vill, hellre usually comes after the finite verb:

• Jag vill hellre stanna hemma
• Hon vill hellre dricka te

So the order is:

• subject + vill
  • hellre
    • infinitive verb

This is a very common Swedish word order pattern.

Both can express wanting, but they differ in tone.

• vill = direct, neutral, common
• skulle vilja = more polite, softer, more like would like

Examples:

• Jag vill ha kaffe. = I want coffee.
• Jag skulle vilja ha kaffe. = I would like coffee.

In everyday speech, vill is often perfectly fine, especially in simple statements like this one.

Because te is usually treated as an uncountable noun, like water in English.

So Swedish often says:

• dricka te = drink tea
• dricka vatten = drink water

If you want to talk about a specific tea or a kind of tea, you might use other structures, but in this sentence plain te is the normal choice.

Yes, many learners notice this.

• i en mugg literally means in a mug
• ur en mugg means out of / from a mug

In the sentence, i en mugg focuses on the tea being contained in a mug. That is understandable and natural enough.

But when talking about the act of drinking, Swedish often prefers:

• dricka te ur en mugg = drink tea from a mug

So:

• te i en mugg = tea that is in a mug
• dricka ur en mugg = drink from a mug

Both can appear, but ur is often more specifically tied to the action of drinking.

Nu means now.

Here it adds immediacy:

• Jag vill ha ett glas kallt vatten nu = I want a glass of cold water now

Its position here is natural. Swedish often puts time words like nu toward the end of the clause, though other placements are possible depending on emphasis.

Men means but.

It connects two main clauses:

1. Jag vill ha ett glas kallt vatten nu
2. hon vill hellre dricka te i en mugg

After men, the next clause starts with the subject hon, so the word order stays normal:

• men hon vill ...

If another element had been placed first after men, then Swedish would use verb-second word order, but here it is straightforward.

Because it comes after the modal verb vill.

In Swedish, modal verbs like these are followed by the infinitive without att:

• vill dricka = want to drink
• kan komma = can come
• ska gå = will / shall go

So:

• hon vill hellre dricka te is correct
• not hon vill hellre att dricka te

Almost, but not exactly.

In Swedish, glas can mean:

• glass as a material
• a drinking glass

So in ett glas kallt vatten, glas means drinking glass.

Context usually makes the meaning clear.

The original sentence is correct, but in conversation a Swede might also say something like:

• Jag vill ha ett glas kallt vatten nu, men hon vill hellre ha te i en mugg.
• Jag vill ha kallt vatten nu, men hon vill hellre dricka te.
• Jag vill ha ett glas kallt vatten, men hon tar hellre te i en mugg.

The exact wording depends on whether the speaker wants to emphasize having the tea, drinking it, or the type of container.