My favourite season

My favourite season is spring, because after a rainy and windy autumn and a grey and freezing winter later, when spring comes, everything wakes up and blossoms. That’s really inspiring and empowers (motivates is a little better here) me for outdoor activities like jogging. Some people say there’s no bad weather, but weak characters (this idiom is a little strange in English. I would say, there's no such thing as bad weahter, only bad clothing). Anyway, I find it difficult to go out running, when it’s dark and piercingly windy – then I have to make do (consider using 'settle for' instead of 'make do with') with a treadmill, which is only a mediocre a poor substitute. So when the first rays of sunshine warm the air, I’m ready for a fresh dose of endorphins (endorphins - plural).

Anyway, your English is very good. The above "corrections" are mostly suggestions.  If you are only looking to improve your style of writing then here are a few suggestions.

The first sentence is a little too long. Consider: My favourite season is Spring. After a rainy, windy Autumn and a freezing Winter (no need to say 'later', most people should know the order of the seasons), everything comes to life and blossoms (or everthing is alive and blossoming). 

Empower is a strong word. Usually you are empowered to do something special. Again, break up your sentence a little. It's inspiring! The Spring motivates me to go outdoors and run!

'Anyway' is typically used if you have strayed from the main point you are making. So it's not entirely necessary here. 

dark and piercingly windy - it's unusual to use adjectives like "piercingly" in this way. You could say 'I find it hard to run in the dark night and piercing wind'. This means your language has balance because you are describing both the night and the wind. But this style of writing is typically used in Novels. A word like "piercingly" typically is used in the past tense and comes after a verb. For example "He spoke piercingly" "He ran rapidly" "She danced slowly". It can be used in other tenses too however "You should walk quickly" "Eat quietly"

"make do with" is not brilliant. People will definitely understand what you mean, but if it's excellent English you want then stay away from it. I have to settle for the treadmill.

A mediocre subsitute - a better idiom is a poor substitute. Mediocre means average or ok. Not great, not terrible.

Anyway, these are all only suggestions!