Sometimes I cover with black plastic sheeting because:
Here comes one vote for covering the soil
Despite many who disagree with me, I cover my empty raised beds with black plastic in the winter as it stops them getting waterlogged and warms the soil nicely in the Spring.
and absolutely agree with:
The trouble with covering to stop weeds growing is that they all suddenly grow when you take the covers off again
Sometimes I leave the beds uncovered because:
all the time the frost breaking it up.
However, this is not strictly true for all soil types:
I would leave it on top for the worms to do their work. Put your feet up you have probably deserved it. In the spring you should just have to give it a light forking over, Saves all that hard work.
because (1) the worms didn't do their work and the manure and compost just sat on the top all winter and (2) because the heavy clay soil had settled and got compacted by rain and needed a mattock rather than a light forking over that spring.
I did think the beds where I had dug trenches and filled with old compost in autumn had better soil texture the following spring.
And to add my pennithworth to the debate LOL, I'm in favour of growing an overwintering green manure rather than leaving beds open to the elements - the roots anchor the soil, the soil isn't half as waterlogged by spring which also helps to warm it up quicker, and thirdly when it is dug into the soil, it will break down and provide the nutrients that summer crops need.