El coche no quiere arrancar cuando hace mucho frío.

No, not literally. In El coche no quiere arrancar, no quiere is an idiomatic, slightly personifying way to say won’t or doesn’t want to.

So:

• El coche no arranca = The car doesn’t start
• El coche no quiere arrancar = The car won’t start / The car just refuses to start

It gives the sentence a more natural, everyday feel, as if the car is being stubborn.

Because arrancar is the usual verb for starting an engine in Spanish.

• arrancar un coche / un motor = to start a car / engine
• empezar = to begin, to start in a more general sense

So for vehicles and engines, arrancar is the normal choice.
A Spanish speaker would much more naturally say:

• El coche no arranca
• No quiere arrancar

than El coche no quiere empezar.

Because in Spanish, after verbs like querer, the next verb goes directly in the infinitive.

Pattern:

• querer + infinitive
• pueder + infinitive
• necesitar + infinitive

Examples:

• Quiero comer = I want to eat
• No puede venir = He/She can’t come
• El coche no quiere arrancar = The car won’t start

English uses to; Spanish does not here.

In Spanish, no normally goes directly before the verb it negates.

So:

• El coche no quiere arrancar
• No tengo tiempo
• No funciona

That is the standard word order for simple negation.

Because hacer frío is the standard Spanish expression for talking about cold weather.

• Hace frío = It’s cold
• Hace mucho frío = It’s very cold

This is different from estar frío, which usually describes a thing or person as cold:

• La sopa está fría = The soup is cold
• Tengo las manos frías = My hands are cold

So for weather, Spanish normally uses hacer:

• Hace calor
• Hace frío
• Hace viento

Because in hace mucho frío, frío is functioning as a noun in the weather expression, and mucho modifies nouns.

Compare:

• mucho frío = a lot of cold / very cold weather
• muy frío = very cold, where frío is an adjective

So:

• Hace mucho frío = correct for weather
• Está muy frío = correct when frío is an adjective describing something

Because this sentence describes a general or repeated situation:

• The car won’t start when it’s very cold

In Spanish, when cuando refers to something habitual or generally true, the present tense is normal:

• Cuando llueve, me quedo en casa = When it rains, I stay home
• Cuando hace calor, abrimos las ventanas = When it’s hot, we open the windows

So cuando hace mucho frío means whenever it is very cold.

Yes, absolutely. That is also correct and very common.

The difference is mainly nuance:

• El coche no arranca... = straightforward, neutral
• El coche no quiere arrancar... = more expressive, as if the car is being difficult

Both are natural. The version with quiere sounds a bit more conversational.

That depends on the variety of Spanish.

In Spain, coche is the most common everyday word for car.

Other common regional words are:

• carro in many parts of Latin America
• auto in some countries
• automóvil is more formal or neutral

Since you’re learning Spanish from Spain, coche is the best everyday choice.

Spanish often uses the definite article more naturally than English does.

Here, El coche refers to the car in a general contextual sense, often meaning my/the car we’re talking about.

Depending on context, Spanish could also say:

• Mi coche no quiere arrancar... = My car won’t start...
• Este coche no quiere arrancar... = This car won’t start...

But El coche is perfectly natural if the car is already understood from context.

Arrancar is pronounced roughly like ah-rrahn-CAR, with a rolled or trilled rr.

A few points:

• a = like the a in father
• rr = a strong rolled r
• stress falls on the last syllable: arranCAR

That double rr is important because it is stronger than a single r.

Yes. Arrancar has several meanings depending on context. Its core idea is often to pull out / tear away / start moving / start an engine.

Examples:

• arrancar el coche = to start the car
• arrancar una hoja = to tear out a page
• el autobús arrancó = the bus pulled away / started moving

In your sentence, because the subject is el coche, the meaning is clearly to start.

Because the stress falls on frí- and the word contains a weak vowel (i) that forms a separate syllable from o.

So it is pronounced:

• frí-o = two syllables

The accent mark shows the correct stress and helps indicate that pronunciation. Without the accent, it would suggest a different stress pattern.