Today I, it is a cold day.

The last month of the year.

This is a sentence fragment and should be combined with the last sentence: "We are in December, the last month of the year."

Normally, during this month, the days are short

and the sun or the light is only a few hours in the skywe only have a few hours of daylight.

Or something like: "and the sun stays in the sky for only a few hours."

Today it also It rained .

On TV the news , they say that the snow has appearsed on the mountains.

"On TV" is understood from "on the news," generally speaking, but you could also write "on the news on TV."

I think that people have problems with his encouragement level.

I'm not sure what you meant to say here. "His encouragement level" indicates that you're referring to a specific person, but you didn't mention anyone before this.

In winter clouds a lot , there are a lot of clouds, so people havare sadness.

I like rain so this today for me is good

"This day" sounds more like we're referring to a specific day in the past or future, and less like we're referring to right now.

Winter dDay

Today It iit’s a cold day.

We are in December.

“We are” is often written as “We’re”.

Normally, in this month, the days are shorter.

“The days are short”, would also be correct but I wasn’t exactly sure of which one you were trying to say.

and tThe sun or the light is only lasts a few hours in the sky

Today it also It rained .

On TV news , the newscaster say id that the snow appearsed on the mountains.

In winter there are clouds a lot , so people havare sadness.

I like rain, so this day for me is good for me.