Any chance of pictures?

I see no reason to pull the plants. If you do that it will definitely not survive the winter ;-) Leave it be and see what it does in the Spring.

Sometimes plants can take a long time to react to stressful conditions. It might be a delayed reaction to the warmer, drier fall. Extended periods of suboptimal conditions can often weaken perennials and make them more susceptible to diseases and fungus and generally overall less resilient. If the soil is well draining, and the majority of the plant is not discolored, you may as well leave it in until the spring. You can prune it back, and prune out the ugly branches, and it might come through. I would give it a shot of fertilizer in early spring to help it along. If you're pretty sure that nothing chemical was sprayed on the plant you can use the ugly leaves in cooking, but it might not have as much flavor as the green leaves.

I'd say just wait it out. I had some yellow spots in Summer, but now that Winter has come around, they're gone. What kind of rosemary plant is the one that you have?