They are all pretty hardy plants. When we get frost, those are plants that we never cover. (save the blankets for the tomatoes, cukes, flowers, etc.) Carrots are super hardy, I still have carrots in my garden and they are fine. One year when I lived in North Battleford, Saskatchewan, Canada (zone 2A) it snowed early and we dug the carrots from frozen ground and they were still ok.
Yup, all of those will be fine.
One of my seed catalogs shows broccoli covered in snow.
I am leaving my carrots all winter, I will pull them in the spring.
Some vegetables, especially root crops taste sweeter after a hard frost because it converts their sugars over.
Some people recommend leaving things like parsnips, turnips and beets until a hard frost just for that reason.
If you leave them until the warm spring temps though the sugars revert back.
Yeah, no need to worry about the broccoli, cabbage, and carrots they'll be fine. They like the cold weather and wont mind a little frost.
If anything the frost will improve the flavor of the vegetables.