If you had a valley on the east side of a continent with high mountains on the north, west, and south; dark clouds continually above the valley.

How would a worlds atmospheric qualities, elevation, and temperature regions be used to cause such a phenomenon?

Would there have to be a strong winds and of what temperature to keep the snow from pilling up? Could the temperature remain warm enough to slowly melt or a warm breeze swoops in from some air current to melt a lot of the snow, but somehow keep the overcast skies?

what I'm looking for is a scientific explanation for an enclosed area that has 24 hour darkness, but during the warmer seasons (when the sun does come out) has constant thick cloud cover with warm enough temperature that the snow may stick a little, but melts over time.

I was thinking about an area where high atmospheric winds carried a consistent rain/snow pattern from extreme heat conditions over a certain part of the ocean that causes a very large evaporation rate in a particular area, thus creating the heavy conditions. However, I'm at a loss to what temperature it's needed to keep these conditions, speed of the wind, and times of a particular year. How far away this boiling like conditions take place or if they should be sun related or geothermal upheaval?

I'm trying to look for an explanation for a valley that is never without clouds, never showing the blue sky. Any help would be appreciated!

I'd also appreciate how the rest of the worlds weather might turn out. I want to stick with our world distance from the sun, single moon, and any other natural aspect of our universe, but if anything needs to be added, I understand. I'm just trying to look for a logical explanation. Thanks!!