Why did Frank?

I don't know why, other than to make him appear to use some zen force or channelling his inner Samurai.

Because your hearing improves when you are using your others senses..

Correction: not using your other senses..

Because when it s dark and your vision is impaired sound mKes it easier to distinguish where the threat was coming from

Your brain only has so many resources. When you're using your eyes, your brain has to process and catalogue everything it sees, which takes up the majority of the "processing power" your brain is devoting to all your senses. It was dark, foggy, and with trees and foliage in the way. So Frank's eyes were pretty much useless.

By closing his eyes, his brain isn't having to concentrate on the information his eyes are bring in. Because of this, the sounds his ears pick up are given a higher priority by his brain, which allows him to focus on where the hitman is.

For me To look Sexier!!!!(as if that's possible)
Seriously when you close your eyes it allows you to see with your hearing by focusing on the environment
He was obscured by trees yet his body was making sounds in the snow etc!!