I must be lucky, as I don't have issues with warping on plywood (much, at least).
I use plywood for inner covers, telescoping covers, migratory covers, solid bottom boards, and D coates nucs. I make sure to cover all of the edges (when possible) with pine wood, securing it with a liberal amount of Tightbond III glue. Then I make sure I cover all exterior edges (and usually a little bit on the inside edges) with two coats of very nice, exterior, durable latex paint. I prefer Sherwin Williams' Duration. It's significantly more expensive than "oops" paint, but you can find it on sale for 50% off or more. At that price, it still isn't cheap, but it's worth every penny in my opinion. I can get 2x or 3x the life out of a piece of equipment with that paint as opposed to the cheapo stuff. Considering that cheap paint will run you about $15 a gallon, if this stuff is $50 a gallon, and I can coat about 24 bottom boards with a gallon, and each bottom board costs me about $8, and with cheapo paint I can get 5 years out of it, and with good paint I can get 10 years out of it, by spending the extra $35 on paint I save $192.
Sorry for the rambling.
But I had a DCoates nuc that I left outside year round in a damp area with extra shade for 14 months now, and it hasnt shown any signs of warping yet.