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Here is a more literate and stylistically verified version of your text.:

The snowfall had not stopped for several hours, hiding all the greenery under its blanket and filling the surroundings with whiteness. The snow crunched under the winged creature's feet, and the blood flowing down its back turned the snow scarlet and left footprints for its pursuers.

Those were the days when mythical creatures existed in the world. Luck has turned away from you since birth: you were born with two eagle wings growing out of the flesh on your back.

Growing up, life seemed to have improved — you found a companion, built a family and had a child. But everything comes to an end. You were running from people with pitchforks, who in a few minutes destroyed your long-term happiness: your house was burned down, your lover was killed, and you were deprived of the opportunity to fly. But the child remained alive, and you desperately tried to save him by running away as far as possible. Until, finally, you collapsed from weakness and pain — an arrow pierced your knee, and you were caught in a sharp net.