Are you West side of the mountains? The Anna's winter over every year here - and I've only helped them out the last couple of years, when some of their favorite plants were lost to a cold snap, replacements needed some time to grow and perform. They've been fine finding protection and food without my intervention other years, many seasons they have startled me in January when I would be doing work around one large winter blooming daphne.

I do keep 4 flood lights on back yard and rear driveway all night, I haven't seen them go to them though, only that they show up at the feeders approx a half hour before daylight. That gives me time to bring feeders in over night if it's going to get down into the 'teens', put them back about 6:30 AM, making sure food with warming calories is never unavailable.

In coldest weather, I mix the ratio of sugar to water stronger, about 1 part sugar to three parts water - and it doesn't freeze as quickly.

Your visitor may be warming himself at your light, or the fixture might give him a good viewpoint to 'guard' his feeder. If you can leave it on at night I would - it may help with warmth, and it can't hurt with your own security. According to the police, outside lights are one of the best theft deterrents going :)

Here is a link that might be useful: Wild Birds Hummer tips - Salem