Guilfordbeekeepers.org

Hey, first year beekeeper here. I have an internal dual-access feeder, and I'm wondering what will happen in the next few days when the temperature gets into the low 20s. At some point, it will get cold enough to freeze and presumably the sugar will precipitate out of the solution. How do the bees cope when this happens?

Bees will not take syrup that is below 50 degrees F and they will cluster at 47 degrees F. The temperature for the next 10 days will not be above 47 per weather.com as of 1300 today for the Whitsett, NC area.
I would remove any syrup that is still on the hive until it warms up to 50 or above.
But your question was : ....the sugar will precipitate out of the solution. How do the bees cope when this happens?
It has been my observation that the bees will take the sugar that is left after the water has evaporated if they can get to it when the temperature is 50 or above. Hope this answered your question.
Ski

I agree with ski,

This is the wrong time of year to have hive top feeders above your bees.

The temperature of the syrup is too cold for the bees to take it.
Plus, the syrup will cause more condensation inside the hive
possibly dripping on the clustering bees, wetting them.
Bees getting wet this time of year could be disastrous.
Leaving them with a good supply of honey for over wintering is best.

I used dry sugar in my hives last year for extra stores with good results.
I'm using dry sugar in my hives again this year.
Here is a link explaining how to use dry sugar in your hives.

Reminder: don't open up your hives unless the bees break cluster.
(when they break cluster you will see bees flying outside the hive)

http://www.bushfarms.com/beesfeeding.htm#drysugar