Yes, they do.
But they feed much slower and are less inclined to chase a bait.
That's why plastic worms, fished very, very slowly across the bottom or just inches above, have always been my winter bait for bass. Larger worms, as long as 12 inches, will get a better bite.
Be prepared for a less aggressive strike, as they will tend to pick the bait up and hold it before swallowing.
This is also the time of year when scent/taste enhancers come into their own. Give that Hot Sauce, Smelly Jelly or Berkley Strike a try.
When the water is cold, it burns more energy to chase a food item than they can get out of eating it.
So you really have to fish an area intensely to get bit.
You pretty much have to hit them on the nose to entice a strike.