Sure, while you can't prove a direct cause-effect, the anecdotal evidence seems rather strong.

I also experienced this same effect after moving to London (from California) in the winter (very cloudy). I felt so low energy for a solid month, and was constantly feeling unwell. Moreover, I had the strangest "cravings" to bask in the sun (such a weird thing to explain, I've never had such an urge before).

The week that I started to figure out my Vitamin D deficiency, I made sure to get a lot of sun every day (it just started getting sunny in London). I noticed immediate improvements.