I've been mousing round the internet. Looks like people are saying
leave the foliage until it is completely died down to the ground, dry and brown, That way you know all the "goodness" has gone into the root-crown.
Then cut it all off about 1 inch off the ground. Leaving the cut "stumps" won't hurt the plant, but it will help "anchor" the mulch you'll be putting on top.
Remove the dried fronds because the dreaded asparagus beetle may have left eggs there, and you don't want to give them a chance come next Spring. Compost the fronds completely n the middle of a hot pile,especially if you've had any bugs.
Now that your ground is bare, absolutely pull up every single weed you see. Asparagus cannot compete successfully with perennial weeds, and here's a good time to get rid of them.
Put a 6 inches deep topping all over the bed, either composted cow manure, or any kind of compost, grass clippings, or tree leaves or straw, whatever you've got. This is important to keep the roots well-insulated over the winter, i.e. to prevent repeated thaw-freeze-thaw-freeze. This is particularly important in raised beds, which are exposed/ vulnerable to repeated freezing and thawing.
Loosen this topping periodically by just raking it up a bit. You don't want it to completely bog down and form an impenetrable mat.
Around about Feb, if your leafmold or whatever has decomposed, go ahead and put on another 6 inches. In the Spring your bed will be "pre-fertilized" from all that compost. Weed any little early-sprouting weed you see, and then you're ready to welcome your first asparagus sprouts!!.
Or so they tell me!
35 posted on 11/07/2014 6:25:34 PM PST by Mrs. Don-o
("Stone cold sober, as a matter of fact.")