Many of the root crops like carrots, turnips, rutabagas, and parsnips can remain in the ground through the fall and into winter as long as the roots are protected from freezing temperatures.
The benefit of leaving them in the garden is that when these vegetables are kept growing during the cool nights of fall, they begin to accumulate more sugar in the roots.
The important thing is to cover them with straw, leaves, blankets, or anything that keeps the roots and soil from freezing while leaving just the green tops exposed. If the "shoulders" of your rutabagas are above ground and exposed, be sure to cover them with soil before mulching them.
A covering of 6"-8" of shredded leaves (up to 12" in colder regions) is perfect protection for these root crops but it should be applied before the first hard freeze.