Vitamin D supplementation at the level of 800 IU per day does not appear to be an effective treatment for Seasonal Affective Disorder in older women.
"Winter depression" is properly known as "Seasonal Affective Disorder" (SAD) or "major recurrent depressive disorder with seasonal pattern". As the name suggests, it's recurrent depression that occurs and remits in sync with the seasons, typically occurring in the winter and remitting in the summer.
Typical treatments include light therapy (involving the daily use of a bright, broad-spectrum light to simulate summertime sunlight. Related question/answer here), cognitive-behavioural therapy, and/or anti-depressant medication, though possible links between vitamin D deficiency (which typically occurs due to lack of UVB exposure, which is common at high latitudes in the winter) and SAD have been investigated.
In a (admittedly small, only 30 participants) study comparing Seasonal Affective Disorder patients against normal controls, no difference in serum vitamin D levels was found.
Another study (though again, small, 29 participants) found the same and also compared the serum vitamin D levels in the SAD group against the same group's levels during the summer. No difference was found there either, suggesting that vitamin D deficiency is not linked to SAD.
A larger study (over 3000 participants) in China also found no link between depressive symptoms and serum vitamin D levels.
Another large (over 2000 participants) study in the UK investigating vitamin D supplementation's effect on preventing SAD symptoms found no significant effect.