I like winter

Today I feel good, but I'm a little tired because I'm getting I get up up early and at night I'm sleep bad I don't sleep well, because there is lot of noise of children playing. (The comma here is incorrect.  This is the end of the sentence.) Another thing that also make noise is the garbage truck; this truck goes ("goes by" or "drives by") three times a week at 6:30 A.M.  Also during the night it's very hot, now that it's summer.

Winter I like, (<-- some people will say you should say "I like winter" but in English you can say "Winter I like".  It is unusual, but you can say that.) because I can to sleep very well.  If I feel cold I can to use ("put on more clothes" is better) more clothes and if I feel warm, I can take off some clothes.

I like winter

Today I feel good, but I'm a little tired because I get up early and I don't sleep well at night. There is lot of noise from children playing. Another source of noise (or something else that makes noise) is the garbage truck; it (this truck) picks up the carbage (or comes by my street) three times a week at 6:30 A.M. Also during the night it's very hot, now that it's summer.
 
I like winter, because I can sleep very well, If I feel cold I can put on more clothes and if I feel warm I can take off some of my clothes.

Notes

If you talk about habits use simple present (I get up, I sleep bad)

"Because" twice in the same sentence doesn't sound good

"Another that also makes noise" = You have to clarify "another" [thing which annoys you or causes problems to your sleep/source of noise, inconvenience]

"Another thing that also makes noise" sounds correct. 

"This track goes..."= to go somewhere is to leave a place/ to come is to arrive. I would use the truck 'passes by' or better 'picks up the carbage'  

I like + object = I like winter (as you wrote in your title!) and similar : I love the sea, I hate bugs....

I can + verb = I can sleep, put on clothes, take off clothes (without to)

I am not a teacher but I hope that was helpful.

Keep up the good work! Best of luck.