Absolutely no need to cover at this time of year - although it will get wet, it needs the air, wind and (occasional) sun to dry it off, the frost to make the soil friable and the birds to get at the slugs and bugs (I frequently see a heron feeding on slugs etc on allotments I pass very early in the morning). Covering the soil at this time of year will only turn the soil sour.
Nearer to planting time you can cover a row or two where you want to sow seeds using a cloche, or failing that with a sheet of black plastic well weighted down with soil along it's sides and ends otherwise the wind will get under it and rip it to shreds and it'll be all over the other allotments and you won't be popular
. Use black plastic as the farmers do because black absorbs heat better and therefore heats the soil a bit more.