Following is an excerpt from a University of Maine publication that answers your question:

What care do I provide for my asparagus in preparation for winter?
After the fronds turn brown, remove them by cutting them off at the base. You then have the choice of leaving the bed bare for the winter and hoping for good snow cover to protect the crowns, or mulching the bed with 4″ – 6″ of straw, shavings, or sawdust. A covering will protect the crowns from heaving and cracking if we get an early spring thaw followed by more freezing temperatures.

The disadvantage of having a mulch on the bed is that it will slow down the emergence of the spears next spring. They will grow right through the mulch, and the mulch will help keep weed growth down. Once all danger of frost is past in the spring, you could rake the mulch off to the side, which will allow the soil to warm up faster and the spears to emerge sooner.

https://extension.umaine.edu/gardening/manual/vegetables/asparagus-faq/

https://extension.umn.edu/fruit/growing-strawberries-home-garden

https://extension.umn.edu/vegetables/growing-carrots-and-parsnips
If our winter is mild enough covering the carrots should protect them enough for harvesting in Dec. if temperatures below freezing are predicted keep checking the soil to make sure the ground isn’t freezing. If the ground freezes you will loose your harvest if you don’t dig them up.

Good luck putting your garden to bed.