每年冬天到后，我一在外面一感受感受到凛冽的风就像想哭泣。

The phrase 每年冬天到后 is grammatically correct.
but I personally feel that using it for people and specific objects sounds more natural.
For example,
王先生到后，我们再出门吧。(After Mr. Wang shows up, let's go out.)
快递到后，我去联系王先生。(After the express arrives, I'll contact Mr. Wang.)


每年冬天到后 can be changed to 每年一到冬天(Every year, when winter comes,...). Sounds more natural. 一到 means 'once it comes'.
I use 每年冬天(each winter), just because it's more concise.

我在加勒比的某个岛屿之一长大。

在……之一 sounds a bit strange.

In my experience, there is a subtle difference between 之一 and 'one of' in English.
之一 is typically used in sentences like A是B之一. It seems weird to say A在B之一.
I looked online for someone who could give me a detailed explanation of the grammatical use of 之一, but I was failed.
therefore, I can only offer my unprofessional judgment:

之一 is actually a shortened version, or abbreviation, of ‘（众多东西）中的一个（东西）’.
之一 =（众多东西）中的一个（东西）
If you substitute this formula into your sentence:
我在加勒比的岛屿之一长大。 = 我*在加勒比的岛屿中的一个*长大。
The part between the asterisks is long, so people often skip the modifier before the "的/之" and look directly at what comes after the "的/之". So your sentence could easily be mistaken for "我在一个长大"(I grew up on one).
Although readers will immediately realize that something has been omitted here, then reads forward and discover that the omitted element is 岛屿(island) and the complete sentence is 我*在加勒比的岛屿中的一个(岛屿)*长大, it is not a common occurrence, and there is always a brief moment of confusion.

So it'll be better to let the "岛屿" come after "的/之" and the quantifier"一个".
You could say:
我在加勒比的一个岛屿长大。
or
我在加勒比的某个岛屿长大。


------------
In addition, the use of A是B之一 has been suggested to be too redundant.
For example, 王先生是贵校之杰出校友之一(Mr. Wang is one of the outstanding alumni of your school) could be changed to 王先生是贵校之杰出校友 for better flow.
If you want to squeeze two pieces of information into one sentence: 1. Mr. Wang is an outstanding alumni, and 2.The school has many outstanding alumni, not just Mr. Wang.
In fact, you can say: 王先生是贵校*诸多*杰出校友之一(Mr. Wang is one of the many outstanding alumni of your school.)

在那里我们只有两种季节：有雨季，还有旱季。

雨季，还有旱季(The rainy season, and the dry season) is a more literary way of saying 雨季和旱季(the rainy season and the dry season), and I personally think 还有 in this case means means "and", not "have".
在那里我们只有两种季节：雨季，还有旱季。 = we only have two seasons: the rainy season, and the dry season.
在那里我们只有两种季节：有雨季，还有旱季。sounds like: we only have two seasons: have the rainy season, and have the dry season. ← a little strange in writing.
but it is fine in speech. You will find native speaker also employ statements like this when they're chatting.

你懂这种情况吗？

对比上面的描述和，冬天的情况就不一样了：寒风凛冽，衣服太重了，白天短太短了...

没有阳光时我的心情变成很难受。

or 没有阳光时我感觉很难受。
or 没有阳光时我的心情变得不太好。

看我写的了我的描述后，你同情吗？

我觉得当然有人同意情。