I'm wondering what would be a good choice for sealing a outdoor hot tub cover made from plywood?
For example, would an outdoor paint or something like tung oil be better for a high heat and humidity situation?
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If the plywood is of the right type it doesn't need to be sealed as far as protecting it goes, exterior-grade plywood is supposed to be resistant as-is. One classification of exterior plywood is WBP which stands for Water and Boil Proof (that's literally how it is tested). The reason to coat your hot tub cover should be to maintain its looks, and if the plywood is not an exterior grade no simple coating can be relied upon to make it last in such an environment1.
would an outdoor paint or something like tung oil be better for a high heat and humidity situation?
Tung oil is, relatively speaking, a poor moisture seal. All straight oils are. Tung has this great rep for being waterproof but it tends to be exaggerated, and when used straight as it is normally applied these days it provides little meaningful protection. If you want to see the plywood a far better choice would be a marine-grade varnish, but be prepared for some sticker shock! I should also mention that it will impart a significant yellow cast to the wood, which some people like and others hate.
Paint may or may not be waterproof. Some paints are, automotive coatings for example are very clearly made to be completely waterproof, others are specifically made to be "breathable" or "micro-porous" and this means water does get through them2. Paint could be a good choice here but you have to pick carefully — assuming the cover is made from a good-quality exterior ply you want to use a breathable paint (which will probably be waterbased), not something like a traditional oil-based enamel.
1 Even solid woods that are naturally resistant to rot begin to look weathered once the finish they are coated with begins to break down from light and moisture exposure, which might take as little as 1-3 years depending on conditions. In the case of something not naturally resistant to water such as interior plywood, the same failure wouldn't just lead to greying/silvering it will begin to bubble and peel apart.
2 The idea being that it can afterwards escape rather than becoming trapped underneath, leading to paint bubbles or flaking and ultimately to the wood beginning to rot.