Walking in the Snow

Last night, it was snowing. It was, in fact, the first snowfall of Shanghai this winter. Therefore, I made the decision to walk to my university. There's approximately 10 kilometers between my house and the campus, so I need 3 hours or so to reach the university by foot. I feel a bit insecure walking there alone, but feeling the snow's embrace is fully worth it.

Thereby is a word used in a sort of cause-and-effect relationship.  Therefore is used when making a decision.  

Thereby - as a result of something.

Therefore - for some reason.

Excellent work on this paragraph.

Snow brings up a lot of memories. The memories of my childhood, for example.

This is not a complete sentence.  There is no verb.  I would recommend combining the two sentences.

"Snow brings up a lot of memories, such as those of my childhood."

I can imagine the snow as it drifts in the air like butterflies or doves. Such thoughts instill a sense of hope and connection with the Earth.

Trees, houses, all manner of things bedecked in a blanket of snow.  Also, use "and" to complete your list.

"Bedecked" in this context is an adjective.  Again, you need a verb.  You could say "Trees, houses, and all manner of things were bedecked in a blanket of snow."

Earth seems almost as if it is hibernating. Building snowmen, throwing snowballs and playing in the snow in general are such memories that come to mind whenever the snow falls.

Good!

However, Shanghai's snow does not remind me of these things. The snow is merely slush. Then I got a cold today.

This is not incorrect, but it's very odd to jump straight from talking about the snow to your cold.  The two sentences share no obvious connection.

Great work.

Walking in the Snow

Last night, it was snowing. It was, in fact, the first snowfall of Shanghai this winter. Therefore, I made the decision to walk to my university. There's (There are or It is (It's)) approximately 10 kilometers between my house and the campus, so I need 3 hours or so to reach the university by foot. I feel a bit insecure walking there alone, but feeling the snow's embrace is fully worth it.

Snow brings up a lot of memories. The memories of my childhood, for example. I can imagine the snow as it drifts in the air like butterflies or doves. Such thoughts instill a sense of hope and connection with the Earth. Trees, houses, all manner of things bedecked in a blanket of snow. Earth seems almost as if it is hibernating. Building snowmen, throwing snowballs and playing in the snow in general are such memories that come to mind whenever the snow falls.

However, Shanghai's snow does not remind me of these things. The snow is merely slush. Then I got a cold today.

Almost perfect - more so than the written proficiency of most native English speakers!  I hope you've recovered from your cold.