Posting to follow because I have the same question. I've looked into "lasagna" beds (layering cardboard and compost) but not sure
how it works in raised beds.
Thanks, cheddarpie. I'm also not sure if it matters what's under the winter cover? I don't want to find out in March that I've been insulating weeds and sand or something!
It doesn't matter. If its weeds then 5 minutes with a hoe will kill them all, its actually better if weed seeds sprout before you plant since its easier to kill them. I regularly put cardboard down on the top, seeds sprout, hit cardboard and then die before reproducing.
Add compost in the fall for optimal results. Add it in the spring if you run out of time. Either way results in better yields, it really doesn't make much yield difference, any compost at any time is great. Remember compost has two parts, the physical and chemical. Chemical is the fertilizers and nutrients, plants regularly consume these as they grow and you eat the vegetables without replacing these vital nutrients. The physical is the fluffy bulking nature of compost, it helps retain water (similar to peat moss, another soil amendment). Sand is also good for some gardens, it breaks up clay which adds drainage so that plant roots won't drown.
For soil its important to add amendments that are useful for what you want to plant. For tomato's I add calcium, for peas I use less nitrogen, for my clay plot I added sand, for my great soil I add fertilizer. For my acidic soil near a spruce tree I added dolomite (a base).
For simplicity just weed and water and whatever you plant will produce. The fancy stuff is for people chasing extra high yields (like 100 tomato's/plant)