How long can I leave a wood fence after pressure washing, before staining it?
Some fences are never stained. Keep in mind that sunlight will "bleach" wood that is not protected from UV light. So, you can leave the fence as-is but it might significantly weather with no protection, depending on whether the pressure washing damages whatever existing finish is on it now.

Also, you don't necessarily want it to be hot when applying an exterior stain. Best time to stain would be a cloudy day. If the stain dries / cures too quickly it could lead to problems. Most exterior stains will instruct you to not expose the stained object to direct sun until the stain cures.