Untreated plywood and oak will rot if heavily exposed to water. You need to switch your thinking to how an outdoor staircase is built. They use rot resistant wood, treated wood, or composite materials.
Marine plywood is a popular idea for water resistance but, due to its chemical composition, it isn't a healthy wood to use in a house. If children spend a lot of time playing on marine wood, they are risking actual poisoning. The symptoms start with mild chemical rashes and get worse from there.
Of your choices composite deck material will last the longest. And there is actual composite stair treads. But I've also built stairs using normal composite deck boards. As long as the under support isn't too far apart two 5ish inch composite boards work very well. See what you have locally. Treated and cedar lumber also works quite well, it just doesn't last as long. Purposed lumber like external stair treads are usually textured for traction.
Also check your local codes, some do not want any treated wood indoors. You may be limited to composite and natural rot resistant wood.
The riser covering the entire opening isn't strictly necessary. Check your local codes, but openings to the rise is often limited to a max opening of less than 4 inches. The purpose of that is to prevent a child from sticking their head in the opening. http://www.co.stevens.wa.us/landservices/documents/STAIRWAYSECTION.pdf
While riser boards provide extra strength to the tread, a 2x12 stair tread doesn't usually need the support. That does depend on the stair design. The riser board is there more for looks, and safety, than strength. If you wish to leave small gaps for drainage, it won't harm the structure of the stairs.