my answer
Black absorbs more EM than white, but black objects also radiate more. All matter above 0 degrees K radiate EM known as "black body radiation". Black objects radiate that energy more quickly than white objects, so they get cold more quickly.
"During the day in a polar region", means that in the dead of winter it's dark out, even at noon. (The question didn't specify the season.) If the sun is below the horizon or very low in the sky (i.e., traveling through a lot of atmosphere), the solar EM wouldn't be much, in which case the black would radiate more energy than the white, and the inside would get colder.
Also, even if there is some sun, the surface of the coat is on the outside of the insulation, so any heat that it absorbs would quickly radiate back out into the air before that heat could penetrate the insulation to help warm you up.
I didn't look any of this up, it all from memory so I can't guarantee it's accuracy.