Yes, your beets survive winter in the ground when temps stay above hard freeze levels with some basic protection in place. Light frost won't hurt your roots at all. In fact your beets will taste sweeter after a few cold nights hit your garden in fall each year.
I left a row of beets in my zone 7 garden one winter just to see what would happen with them. With a thick layer of straw on top they made it all the way to January without any damage at all. I pulled fresh sweet roots from frozen ground while snow sat on the mulch above them.
Beets are biennials which means they need two years to complete their life cycle and set seed. This makes them tough against cold since they expect to live through winter in nature. Your plants convert starches to sugars when temps drop which protects cells from ice damage and makes roots taste better too.
The beets cold tolerance has limits though so you need to know where yours end in your climate. Light frost below 32°F (0°C) is no problem at all for your roots in the ground. Hard freezes below 25°F (-4°C) start to cause damage that turns roots mushy when they thaw out later on.
My neighbor tried overwintering beets without any mulch cover on them last winter in our area. Her roots turned to mush after our first hard freeze hit that December. The unprotected soil froze solid and killed everything still in the ground that cold week.
Pile 6-8 inches of straw mulch over your beet bed before hard freezes arrive in your area each fall. This thick layer keeps soil from freezing solid even when air temps drop well below zero outside. You can pull back the mulch any time during winter and dig up fresh roots for dinner whenever you want.
If you live in zones 3-5 with severe winters you may want to harvest before ground freezes solid instead of risking your whole crop. Winter beet storage works great in a root cellar or cold garage where temps stay between 32-40°F (0-4°C) all season. Roots keep for months this way without any fuss or worry.
Gardeners in zones 8-11 can grow beets right through winter as a cool season crop with no extra work at all. Plant in fall when summer heat breaks and harvest all winter long without any protection needed. Your mild climate lets you skip mulching and just enjoy fresh beets whenever you want them from your garden.
Read the full article: Growing Beets for Sweet Roots and Greens