chuwoseo soni tteollyeoyo.

Because 춥다 is a ㅂ-irregular adjective.

When a ㅂ-irregular stem is followed by a vowel-starting ending like -어서, the ㅂ changes to 우:

• 춥다 → 추워서
• 덥다 → 더워서
• 어렵다 → 어려워서

So:

• 춥다 + -어서 → 추워서

This is one of the first irregular patterns Korean learners meet.

Here, -아서/-어서 means because or so. It connects the reason to the result.

So the structure is:

• 추워서 = because it’s cold / because I’m cold
• 손이 떨려요 = my hands are trembling

In this sentence, -서 gives the cause of the trembling.

It can feel like either in English, and that is normal.

Korean often leaves the subject unstated when it is obvious from context. So 추워서 can be understood as:

• because it’s cold
• because I’m cold

In this sentence, both lead to basically the same idea. Korean does not always force you to choose as explicitly as English does.

Because Korean often omits possessives with body parts when the owner is obvious.

So instead of saying my hands, Korean very naturally just says:

• 손이 떨려요 = the hands are trembling

But in context, it is understood as my hands.

You could say 제 손이 떨려요, but that would usually sound more explicit than necessary unless you are emphasizing that it is your hands, not someone else’s.

Because 손 is the thing that is trembling, so it is marked as the subject.

With 떨리다, the body part experiencing the action/state takes 이/가:

• 손이 떨려요 = the hand(s) tremble
• 다리가 떨려요 = the legs are shaking
• 목소리가 떨려요 = the voice is trembling

If you used 손을, it would suggest a different sentence structure and would not sound natural here.

Korean nouns usually do not have to show singular vs. plural the way English does.

So 손이 can mean:

• a hand
• hands

depending on context.

In this sentence, English often uses hands because that is the natural translation in context. Korean does not need to mark the plural unless it really matters.

If you wanted to be more specific, you could say:

• 두 손이 떨려요 = both hands are trembling

The base form is 떨리다.

Its polite present form is made like this:

• 떨리다
• 떨리어요
• 떨려요 (contracted, and much more common)

So 떨려요 is the normal spoken form.

Both relate to trembling or shaking, but 떨리다 is very common when something trembles involuntarily, especially a body part, voice, or the body itself.

Examples:

• 손이 떨려요 = my hands are trembling
• 목소리가 떨려요 = my voice is trembling

떨다 also exists and means to tremble/shake, but in this kind of sentence, 떨리다 sounds more natural and idiomatic to many speakers.

So for a learner, 손이 떨려요 is a very useful pattern to remember.

Because Korean often uses the simple present form for a current ongoing state, especially with symptoms or bodily conditions.

So:

• 손이 떨려요 already naturally means my hands are shaking
• 손이 떨리고 있어요 is also possible, but it sounds more explicitly progressive

In everyday speech, 떨려요 is usually the more natural choice here.

It is the informal polite style, often called 해요체.

That means it is polite and very commonly used in everyday conversation.

Compare:

• 떨려요 = polite everyday style
• 떨려 = casual/intimate
• 떨립니다 = formal polite

So this sentence is appropriate for normal polite conversation.

Yes.

떨리다 can be used for trembling caused by:

• cold
• fear
• nervousness
• excitement
• illness

So 손이 떨려요 by itself could mean your hands are trembling for different reasons. In this sentence, 추워서 makes the cause clear: the trembling is because of the cold.

Yes, it sounds natural.

It is a very normal kind of Korean sentence:

• reason + 서
• body part + 이/가
• state verb

It is concise, natural, and very typical of spoken Korean. A native speaker would easily understand it.