In this case, 「つめたい かぜの ふく」 is a noun modifier⁽¹⁾⁽²⁾ for 日.

Basically, the verb clause the precedes the noun modifies it in a similar way to "that" in English. For example (from the references above):

ボブは、いつも勉強する人だ。
= Bob is an always-does-studying person.
= Bob is a person who always studies.

In the same way, 「つめたい かぜの ふく」 is modifying 日.

つめたい かぜの ふく 日
= cold-wind-blows day
= day that a cold wind blew

You are correct that the phrase is ある日, but the day is qualified by saying what kind of day it is. (That is, it is a day when a cold wind is blowing.)

ある つめたい かぜの ふく ひ
= One cold-wind-blowing day

Keep in mind that having a 。 at the end does not translate as a sentence to English, but marks the end of a clause. (i.e. In this context you would not just say "One day.")

ある つめたい かぜの ふく ひ。・・・
= One cold, windy day, ...

In this case, 「つめたい かぜの ふく」 is a noun modifier⁽¹⁾⁽²⁾ for 日.

Basically, the verb clause the precedes the noun modifies it in a similar way to "that" in English. For example (from the references above):

ボブは、いつも勉強する人だ。
= Bob is an always-does-studying person.
= Bob is a person who always studies.

In the same way, 「つめたい かぜの ふく」 is modifying 日.

つめたい かぜの ふく 日
= cold-wind-blows day
= day that a cold wind blew

You are correct that the phrase is ある日, but the day is qualified by saying what kind of day it is. (That is, it is a day when a cold wind is blowing.)

ある つめたい かぜの ふく ひ
= One cold-wind-blowing day

Keep in mind that having a 。 at the end does not translate as a sentence to English, but marks the end of a clause. (i.e. In this context you would not just say "One day.")

ある つめたい かぜの ふく ひ。・・・
= One cold, windy day, ...

In this case, 「つめたい かぜの ふく」 is a noun modifier⁽¹⁾⁽²⁾ for 日.

Basically, the verb clause the precedes the noun modifies it in a similar way to "that" in English. For example (from the references above):

ボブは、いつも勉強する人だ。
= Bob is an always-does-studying person.
= Bob is a person who always studies.

In the same way, 「つめたい かぜの ふく」 is modifying 日.

つめたい かぜの ふく 日
= cold-wind-blows day
= day that a cold wind blew

You are correct that the phrase is ある日, but the day is qualified by saying what kind of day it is. (That is, it is a day when a cold wind is blowing.)

ある つめたい かぜの ふく ひ
= One cold-wind-blowing day

Keep in mind that this shouldn't have a 。 at the end! It does not stand alone. (In this context you would not just say 「ある日。」, as you would not just say "One day.")

ある つめたい かぜの ふく ひ、・・・
= One cold, windy day, ...

In this case, 「つめたい かぜの ふく」 is a noun modifier⁽¹⁾⁽²⁾ for 日.

Basically, the verb clause the precedes the noun modifies it in a similar way to "that" in English. For example (from the references above):

ボブは、いつも勉強する人だ。
= Bob is an always-does-studying person.
= Bob is a person who always studies.

In the same way, 「つめたい かぜの ふく」 is modifying 日.

つめたい かぜの ふく 日
= cold-wind-blows day
= day that a cold wind blew

You are correct that the phrase is ある日, but the day is qualified by saying what kind of day it is. (That is, it is a day when a cold wind is blowing.)

ある つめたい かぜの ふく ひ
= One cold-wind-blowing day

Keep in mind that having a 。 at the end does not translate as a sentence to English, but marks the end of a clause. (i.e. In this context you would not just say "One day.")

ある つめたい かぜの ふく ひ。・・・
= One cold, windy day, ...