It is always dark in the hive. They continue with all activities other than foraging. They feed the young, clean the house, process the honey, ETC. The only thing that changes is the outside activity. They sleep in shifts day and night.
Funny, until I read this question, I realized I wondered that too. I often look at the beehives from the window at night and wondered if they are resting in a cluster or moving about. Glad to have found the answer to the question. Thanks, Iddee.