My home city is in the Mideast part ofcentral China.

in northern China
in southern China
in the eastern region of China
in the western region of China

Many people here spend their Chinese New Year on Hainan island.

Using "their" gives the impression that there is a special difference between what you do and what other people do.
For example: I spend my Chinese New Year with my parents, while my brothers spend theirs traveling to a sunny spot. I wish they were here with the family.

I went there on 29th January and went back on 5th(left/went home/went back home) (or) stayed until February 5th.

The temperature in Danzhou is always 12 degrees higher than that in my city.

But on rainy days, I don't feel much warmer, instead I feel almost feel the same as in my city.

almost describes "the same" so needs to be in front of that word

If it is 17 degrees in my city, it feels pretty(a lot/a little/somewhat) warmer.

pretty not used with comparative or superlative
pretty warm
pretty big
pretty happy
pretty old
pretty good

So, if it rains a lot during the Chinese New Year, it is not a big difference to spend the holiday on the northern part of Hainan island or in my home city.

My home city is in the Mmid-eastern part of China.

There are several ways to say this, but Mideast sounds a bit strange to my ears

DuringIn winter, the coldest temperature here is around 6 degrees Celsius.

I went there on the 29th of January and went back on 5thleft on the 5th of February.

I don't feel like it is much warmer in Danzhou.

Unless you are writing something very formal, it is sounds more natural to write it's instead of it is.

If it is 17 degrees in my city, it feels prettyquite a bit warmer.

Pretty warmer doesn't work, you could say pretty warm.

So, if it rains a lot during the Chinese New Year, ithere is not a big difference tobetween spending the holiday on the northern part of Hainan island or in my home city.