Photographing Snowy Owls while it is snowing can be a bit challenging. If you are lucky, the sky may not be too grey, with a bit of diffuse light getting through. Otherwise, the scene is so monotone as to erase many of the bird's and background details.
Post production in this situation was a little easier - not all the fine details were washed out after applying some colour correction.
Watch out for the eyes. In these low light winter situations, the eyes usually turn dark orange when you correct the image. Try to convert the orange to a more natural yellow, if you can.
Cropped vertically in a non-standard size format for composition purposes due to the top of the extended wing being soo close to the top of the frame.
If the bird is perched and not moving, you can try changing shutter speeds, especially much slower speeds, to increase the illusion of more and bigger snowflakes in the background.
Taken handheld with my usual Canon 5D Mark III with 500L f4 lens.
Cheers,
Mike