The First Snow ofIn My Living City

"In My City" is clearer and natural.
Good job capitalizing your title.

I am watching through the window, the ground has been white already, and the cars parkinged beside the road are covered with snow.

"cars parked" Correct participle form.

It is so beautiful and gives me a quiet feeling.

You can also say: "It is so beautiful and gives me a sense of peace."

Cars passed the road beside our house occasionally, leftaving deep tire tracks in the fresh snow.

"leaving" Better continuous action description.

The kindergarten across the street still has its lights on, and there are people are working inside.

Add the street for clarity
"people are working inside" sounds smoother.

I opened a weather forecast APPapp and noticed that the snow will not stop until the day after tomorrow.

"app" Standard capitalization.

I have no idea if the high speed way will be closed tomorrow and whether I could drive back to my work city.

"highway" Correct word.

My wife told me safety icomes first, and I completely agree with her.

"safety comes first" More natural phrasing.

So I don't worry about whether I couldan go back to work anymore, i. If I couldan't , I will just take a day off.

"whether I can" Present tense consistency.
Split into two sentences for clarity.
"if I can't" Present tense consistency.

The First Snow of My Living Cityin the City where I Live

There are different ways to write your title. I tried to think of one that was a little poetic like the text.
"My City" doesn't echo the wording you use in Chinese.

I am watching through the window, ; the ground has been white alreadyis already white, and the cars parkinged beside the road are covered with snow.

"parking" would mean they are in the process of parking; they are moving.

Cars passed occasionally on the road beside our house occasionally, left, leaving deep tire tracks in the fresh snow.

I think it is best to describe everything in the present tense because it is what you are seeing. ("I am watching...")

I opened a weather forecast APPapp and noticedsee that the snow will not stop until the day after tomorrow.

"notice" suggests that you were not searching for that information. But in this situation, I infer that you opened it to find information about the snow, so it was intentional.

I have no idea if the high speed way will be closed tomorrow and whether I could drive back to my work citywill be able to drive to work.

I took out words that did not add essential information and replaced them with words to clarify what the concern is.

My wife told me safety is first, and I completely agree with her.

So, I don't worry whether I could go back to work anymore,have stopped worrying about whether I can go to work; if I couldan't , I will take a day off.

The First Snow of My Living City

Cars passed the road beside our house occasionally, and left deep tire tracks in the fresh snow.

I opened a weather forecast APPapp, and noticed that the snow will not stop until the day after tomorrow.

I have no idea if the high speed way will be closed tomorrow, and whether I could drive back to my work citythe city where I work.

So I don't worry whether I could go back to work anymore, if I couldan't , I will take a day off.

The First Snow of My Living City

I'm not sure what you mean by "Living City"...perhaps you mean the city that you live in? You can just say "My City" and it will mean the same thing.

I am watching through the window, t. The ground has beenis white already and the cars parking beside the road are covered with snow.

It's probably best to make this two separate sentences.

Cars passedSome cars drove down the road beside our house occasionally, and left deep tire tracks in the fresh snow.

I opened a weather forecast APPapp and noticed that the snow will not stop until the day after tomorrow.

I have no idea if the high speed way will be closed tomorrow and whether I could drive back to my work city.the city where I work.

We typically call the major route that you're referencing a "highway", at least where I live.
You can say "the city where I work" - we don't typically say "living city" and "work city".

My wife told me that safety icomes first, and I completely agree with her.

So I don''m not worryied about whether I cshould go back to work anymore, i. If I cshouldn't , I will take a day off.