What do you do with old mulch that had been left on top of annual flower beds or vegetable beds during the winter? Note that this is a different issue from that of what to do in garden beds that contain live plants (albeit perhaps dormant) right through the winter, where the focus of the question is primarily on the plants.
The present FAQ, by contrast, relates to empty beds (living plant material has either died or has been harvested), and the question focuses on the mulch: specifically, whether the old mulch is still viable–and, if so, what you should do with it. This pertains to the biodegradable material (bark, leaves, straw, etc.), not to mulches that do not break down readily (stone, plastic, etc.).
Is Old Mulch Still Good to Use?
Vegetable garden beds and annual flower beds will not have plants in them during the winter but are mulched in fall to protect their soil from the harsh elements in winter. You have worked hard to build up the fertility of your garden soil, so you would not want gusty winds or torrents of water carrying any of it off, would you?
If the condition of the old mulch has not decomposed appreciably by the time spring comes, it will still be usable. How do you determine its condition? Well, scoop up some of the mulch in your hands. Has it more or less broken down into fine particles, so that it is no longer clearly distinguishable from dirt? In that case, it will no longer function very effectively as a mulch; it is time to replace it. If, however, it has mostly retained the look and feel that it originally had, then you can re-use it. The one exception would be if your plants in this garden bed had experienced disease problems last year that you think can be traced back to the mulch; in which case you would want to remove and dispose of said mulch properly (check with the officials in your town to determine a proper way to dispose of such material).
If upon inspection, you decide that the old mulch has not, in fact, decomposed appreciably, you should rake the old mulch aside for now so that you can prepare the planting bed. If you need to get it out of the way, shovel the mulch into a wheelbarrow, dumping successive loads onto a tarp off to the side. Apply compost onto the vegetable garden bed or annual flower bed, and till it under or work it into the soil with a spade.
Now you can see why the first instruction was to rake the old mulch aside: in the course of rototilling or spading the compost into the garden, the old mulch would have been tilled or spaded under, forcing you to acquire and apply new mulch. That would be a waste of time, energy, and money.
Now put the old mulch back onto the planting bed.
This whole process can be completed well in advance of planting time. When it is time to plant, gently remove the mulch from just the area where you are sowing seeds or transplanting plants. With the mulch already in place in this manner, weeds never get much of a chance to emerge.
But what if the old mulch has, in fact, decomposed appreciably over the course of the winter? In that case, work it into the ground as organic matter so that it can serve as a soil amendment, along with the compost. Then acquire a load of new mulch as a replacement.
What About "Living" Mulches (AKA Cover Crops)?
Although "cover crops" (which are so-called "living mulches) is terminology more often heard in agricultural circles than in landscaping circles, some homeowners may find cover crops quite helpful.
Cover crops are sowed over vegetable gardens and annual flower beds in the fall to protect them in winter. When spring returns and you are getting ready to plant again, you need to get a cover crop out of the way. But you can kill two birds with one stone: tilling cover crops under both frees up the garden for spring planting and puts nutrients into the soil.
Mow cover crops first, then run a garden tiller over the garden -- a process known as "tilling under" the cover crops. By mowing first, the garden tilling will go easier, since you will be tilling shorter vegetation. After mowing, spread compost over the same garden bed, and till that under, too, just as you would with any beds that did not have cover crops.