Çok soğuk su içince boğazın ağrıyabilir.

İçince comes from the verb içmek (to drink).

• verb stem: iç-
• suffix: -ince / -ınca

So içince means when (someone) drinks, once (someone) drinks, or sometimes if (someone) drinks, depending on context.

In this sentence, it means something like when/if you drink very cold water.

It can be either, depending on context.

Here it has a warning-like meaning, so English might translate it as:

• when you drink very cold water
• if you drink very cold water

Turkish -ince often gives the sense of when/once/whenever, but in practical use it can overlap with if in sentences like this.

A slightly more clearly conditional version would be:

• Çok soğuk su içersen boğazın ağrıyabilir.

That is more directly If you drink very cold water, your throat may hurt.

Because boğazın means your throat.

The ending -ın here is the 2nd person singular possessive suffix. So:

• boğaz = throat
• boğazın = your throat

In Turkish, body parts are very often marked with a possessive suffix:

• Başım ağrıyor. = My head hurts.
• Kolun ağrıyor mu? = Does your arm hurt?

So boğazın ağrıyabilir is the natural way to say your throat may hurt.

Because Turkish often leaves pronouns out when the meaning is already clear.

In this sentence, boğazın already tells us the throat belongs to you, so senin is not necessary.

You could say:

• Senin boğazın ağrıyabilir.

But that sounds more emphatic, like your throat specifically. Normally, Turkish prefers the shorter version:

• boğazın ağrıyabilir

Yes.

In boğazın ağrıyabilir, the thing that may hurt is your throat, so boğazın is the subject.

Turkish subjects do not need a special ending. The possessive ending -ın does not make it an object; it only means your.

So the structure is basically:

• boğazın = your throat
• ağrıyabilir = may hurt

Ağrıyabilir means may hurt, can hurt, or might ache.

It comes from ağrımak (to hurt / to ache). Its structure is:

• ağrı- = verb base
• -y- = buffer consonant
• -abil- = ability/possibility suffix (can / may)
• -ir = aorist/general tense ending

So:

• ağrır = hurts / will hurt / tends to hurt
• ağrıyabilir = may hurt / can hurt

Here, ağrıyabilir makes the sentence less absolute and more like a possibility or warning.

The y is a buffer consonant.

Turkish often inserts y when a word ending in a vowel is followed by a suffix starting with a vowel.

Here the verb base ends in a vowel sound:

• ağrı-

And the next suffix begins with a vowel:

• -abil-

So Turkish inserts y to make pronunciation smoother:

• ağrı + abil → ağrıyabil-

This is very common in Turkish.

Because su is an indefinite/general direct object here.

• çok soğuk su içmek = to drink very cold water
• suyu içmek = to drink the water

Turkish usually adds the accusative ending -(y)ı / -(y)i / -(y)u / -(y)ü only when the object is specific/definite.

So:

• Çok soğuk su içince... = when you drink very cold water
• Çok soğuk suyu içince... = when you drink the very cold water / that very cold water

The version in your sentence is the more natural one for a general statement.

Here it means very.

That is because it modifies the adjective soğuk:

• çok soğuk = very cold

So:

• çok soğuk su = very cold water

Turkish çok can mean both very and much/many. The meaning depends on what it modifies.

Examples:

• çok soğuk = very cold
• çok su = a lot of water

Turkish very often puts a time/condition clause first and the main result second.

So this order is very natural:

• Çok soğuk su içince = when/if you drink very cold water
• boğazın ağrıyabilir = your throat may hurt

This pattern is common in Turkish:

• Eve gelince beni ara. = When you get home, call me.
• Yemek yiyince daha iyi hissediyorum. = I feel better when I eat.

So the sentence sounds natural and standard as written.

The difference is mainly certainty.

• boğazın ağrır = your throat hurts / will hurt / tends to hurt
• boğazın ağrıyabilir = your throat may hurt / might hurt

So ağrıyabilir is softer and less definite. It suggests a possibility, not a guaranteed result.

That makes it a good choice in a sentence giving advice or a warning.

Yes.

A very similar sentence is:

• Çok soğuk su içersen boğazın ağrıyabilir.

That version is more directly if you drink...

The original sentence with içince sounds a little more like when you do that / when that happens. In everyday use, both can work in this kind of warning.

Yes, several suffixes change form because of vowel harmony.

Examples:

• iç- + -ince → içince
• boğaz + -ın → boğazın
• ağrı + -yabil + -ir → ağrıyabilir

The exact vowel in each suffix depends on the vowels in the word it attaches to. This is one of the most important patterns in Turkish grammar, and this sentence shows it clearly.