As the winter evening grew

[Bassim]

I am wondering if my sentences are grammatically correct.

As the winter evening grew darker, a lonely man was trudging through the snowy empty streets. His head tucked under the collar of his dark coat, he looked neither right nor left but walked purposefully, as a man on an important mission.

 

[Tarheel]

I would delete "lonely" there. You could say:

As the winter evening grew darker, a man was trudging alone through the snowy empty streets.

You could phrase it that way if you want to emphasize that he is by himself (which apparently is the case).