I can only speak regarding basil...but it seems like moving them indoors for frosts is a good idea. Last year I planted some basil in the ground; even though I covered it with frost-cloth AND surrounded it with some of the non-LED christmas lights, it still croaked. Of course, they weren't looking too healthy at that point anyhow because there were critters munching on the delicious leaves, too. So maybe that's just my experience! :)

Basil only really likes heat and is an annual. You may want to plant some new basil, preferably a mini-variety, in a pot, for the house, for winter. It pouts after about November first, until it warms up.
Just about all the other herbs grow great through the winter around here, especially cilantro, fennel,parsley and thyme. Cilantro is an annual and short lived so succession plant it every few weeks. Parsley is a biannual so it will go to seed. Let it go to seed as it will attract butterflies and Benificials to your garden, same with the fennel, some of the best for attracting good guys and butterflies. Just plant more.
Rosemary, lavender and oregano are practically native here and very happy in the ground. Same with sage, I'd start them in the fall or winter to give them the best start. My rosemary was started from a mini-Christmas tree after Christmas.
thyme and mint don't like the hot summer much but will thrive all winter into the early summer. Try chocolate mint and lemon thyme for beautiful and delicious varieties.
For a really elegant, ornamental grass that will thrive in our heat and need little care, try rooting some lemon grass from the Asian grocery. You'll have all the lemon grass you need for tea and Thai recipes. It's very well behaved and a lovely, drapey bunch grass.
I'm going to try some ginger from ginger root and horseradish from the grocery store next. The horseradish can be invasive, although isn't supposed to thrive in our climate so I'm not too worried.
I love having herbs growing all around the yard. They attract beneficials and it's wonderful to collect bunches of herbs fresh from the garden when I'm ready to make a meal.

Tracydr - thank you!! Tell me how the ginger goes. I remember it all over Hawaii, it's such a beautiful plant! I have the lemon grass, and it is wonderfully well behaved, and a great shape. Thanks for the info on the basil - I will plant some for indoors, and bring it out in the spring.