Never deliberately emptied ours for cleaning. And winter is when they get filled for Spring use.

The algae usually only occurs in water butts without lids, or where the sun's been able to get inside the container somehow. The advice is to clean out water butts yearly or bi yearly, depending on conditions, and cleaning out usually just involves swilling it out. In your case, though, it sounds as though you need to give it a good scrubbing with soap and then rinse it out when it's clean. Filters over the drainpipe help to keep the water clean, and you can also use non chemical treatments such as Biotal Refresh Rainwater Treatment.

Useful question and answers...
I've added to GoYpedia :o)

Clean ours out every five or ten years, if necessary. No lid and I use it to soak clay pots before cleaning.

Do you need to re-site for practical reasons?
If you do then it would be preferable to do so before the winter rains so that it fills up again before you need the water. May be worth holding on for a couple of weeks - we could still get an Indian summer and you'd have no water stored.