The best time to do this work is JULY-AUGUST. I have power washed and stained many a deck and fence over the years and the absolute best quality job is done in the hottest months. Depending on how bad the mold and mildew is on the wood you might get away with a simple bleach and water mixture sprayed on the wood to help "bleach" the wood back to a natural color plus remove the mold. Power wash it enough to take away what you want but not too much pressure because you can split and tear the wood apart easily. Then let it sit in the baking sun for several days to let the wood dry to the core. This will let the maximum amount of penetration for the stain / waterproofing to soak in. Do this process every few years and the wood will last a long time. Don't do it or do a bad quality job and you are replacing the fence, deck, swing and such. Trust me some sweat and stain is a LOT cheaper than lumber and cost to replace.

I have a power washer you can borrow when the time comes if you need one