It is already winter and it is getting colder and colder.

This reminds me of thosee good old days when I was a child.

"the good old days" is what I'm used to hearing

During the winter, in the countryside, the skin on children’s faces and hands usually getbegins to cracked.

We need to emphasize it's the skin (not the faces and hands themselves) that are cracking, and "get cracked" is correct but childish, and we usually say "begins to crack".

So every family prepared two kinds of skin care products, one was Bbalsam and another one was clam oil.

In my opinion, balsam didoesn’t have much effect on protecting skin.

While it's grammatical to write "didn't", it's past tense, so it implies your opinion has changed, and now you feel balsam has an effect.

When your face or hand cracked,s, you put some clam oil on them, then maybe two or three days later, the skin of your face or hands would be completely cured.

In my case, I rarely used balsam because I didon’t think it had any function toactually protects the skin.

I don't think "...I didn’t think it had any function to protect the skin" is correct. It could be "...I don't think it functions as a skin protector" but that's too formal.

But the clam oil wais very good at protecting the skin.

However, these two kinds of skin -protectiong products are hard to find nowadays, but decades ago, they were the only two kinds of skin care products available in rural areas.

I suggest using a compound adjective: skin-protection products (although I don't think what you wrote is incorrect). The logic seems clearer to me with the added word "available".

During the winter, in the countryside, children’s faces and hands usually geot cracked.

Technically, what you wrote is correct, but because you were talking about the past, and continue talking about the past in the next sentence, it seems to me this sentence would be more natural if it were also in the past.

So every family prepared two kinds of skin care products, o. One was Balsam and an, the other one was clam oil.

Edited to make it sound natural, but yours is technically correct.

When your face or hands cracked, if you put some clam oil on them, theit, in maybe two or three days later, the skin of your face or hands would be completely cured.

Or:

"When your face and hands cracked, if you put some clam oil on them..."

In my case, I rarely used balsam because I didn’t think it had any function to protecteffect on the skin.

Your sentence is grammatically correct. Mine is more natural.

It's only has some fragrancet.

However, these two kinds of skin -protecting products are hard to find nowadays, but decades ago, they were the only two kinds of skin care products available in rural areas.