It depends on the barn’s set-up. I’ve done it a few different ways…
Where we are now, every stall has a hose and shut-off valve for water. So I start at one stall, dump buckets into a muck bucket on a cart (actually for soaking another horse’s hay, but then I scrub it and rinse it out at the end of cleaning water buckets), but I make sure to leave a few inches of water to scrub and rinse with, then rehang. I fill those buckets while I work on scrubbing the stall next door, so I can keep an eye on them to not overfill, and work my way down the aisle. This particular barn has drains in the aisle, so every few stalls I dump the muck bucket into the drains.
At previous barns with just one hose, I’d dump and scrub them all at once, or in sections for a large number of horses who are stalled, and then refill as I clean stalls. If I’m dumping a bunch, then the wheelbarrow is a must, and then I can wheel all of that water away to a safe place. There’s a trick to getting the hose to stay in the bucket (by wrapping it around the handle on the bucket a specific way that I’m not eloquent enough to describe), but this means you don’t waste time. If you’re really good, you know to leave the nozzle near where you want the water level to be, so that when the bucket is almost full, you no longer hear the water gushing, and that’s your sign to go shut it off and move the hose over.
Dumping, scrubbing, and refilling water buckets for my trainer’s 10 horses, with 2 buckets each, takes me 20 minutes with decent water pressure. I’ve done it faster with more horses and better water pressure.
A BIG help is scrubbing them every day. And I honestly can’t stomach when they don’t get scrubbed every day, because water should not be brown. Our horses seem to agree, as they noticeably drink less if the buckets aren’t as clean.
In the winter, I cut them down to 1 bucket per horse, in order to keep the water thawed easier (much easier to keep warm water coming to 1 bucket that they are drinking from regularly), and that of course helps with time management, too!