I'm assuming you mean a wool cutting or polishing pad and not some type of sheepskin or lambswool wash mitt or wash pad?
If so, historically wool pads are simply spurred and put back to work again. I've never hand washed a wool cutting pad, simply spurred it while spinning it on a rotary buffer and then put it back to use.
I've never used a wool polishing pad because it just doesn't make any sense since foam pads were introduced in 1965, before I was born and there's no reason to follow a wool cutting pad with another pad that's simply going to inflict swirls into the paint when you can use foam instead.
If you want to hand wash a wool cutting or polishing pad you could, it wouldn't be any more different than washing a foam pad by hand. Just soak in a bucket of water with some type of pad cleaning solution, swish it around a bunch, maybe use your fingers to agitate the fibers and then rinse well with running water or in a bucket of clean water and then spin it on your rotary buffer to sling out all the water. (Don't do this anywhere you don't want water-sling. You could also hold the spinning pad inside an empty bucket, a box or anything that has room to hold it to capture all the water that slings out so you don't sling it all over your car, yourself or the wall.
Then spur with a steel spur to fluff the fibers.
Of course, a pad washer is another option and anyone that uses wool pads all the time should really look into getting a pad washer as they are the fastest and best way to clean a wool pad used for heavy cutting and then be able to instantly put it back to work buffing.