You can use Exterior grade (there are two of them - one exterior grade is for brief exposure - like the material pile being outside during construction - the other exterior grade is intended to be exterior facing, its more expensive, and the ONLY kind of plywood you should consider). It will still need to be primed and painted - or painted with a really good exterior paint, likely twice, if you expect it to hold up.
Because its PT (pressure treated), you will need to use special screws and nails. Personally, I recommend screws. More expensive, not as quick to put in, but they hold MUCH better.
For the price, I used Hardieboard, which was essentially the same cost (w/i $1 per 32 sq ft) as plywood at the time, and lasts MUCH longer. Its also not an attractant to things like termites. It will suck up the first coat of paint like a sponge, and the second coat goes on solid - no bubbles, blisters, peeling or "show" as you can get when painting over a knot or a piece of wood with real obvious grain, as the trapped moisture tries to move in and out with the weather.
Those are the plus column.
Lets talk about the minuses.
Its HEAVY. When the wind blows, that's probably a good thing, but if you are all alone, manhandling sheets of the stuff onto saw horses, the frame of your hen house, etc, its a beast. Got to be at least 50% heavier than plywood of similar thickness.
Its HARD. You can pretty well forget throwing a torx bit in the old screw driver, and setting sharp point screws quick as you want into the Hardieboard. I held my board in place with clamps, marked my screw locations, then held a sharp point exterior screw where I wanted it and hit it with a hammer first to set it in place, then came back and finished them all with the screw driver. If you have a torque driver, its not so bad. If you have to pull a screw out for any reason, you will find its once sharp point rounded and dull, like you scraped it on concrete for a bit - because you did.
They claim it cuts like plywood and you need no special tools. While that's true, if you are cutting a lot of it, bite the bullet and buy the special circular saw blades. Otherwise, plan your hen house to minimize cuts, and sacrifice some cheap blades.
Finally, wear a mask. yes, you should wear a mask cutting PT lumber, too - but PT lumber doesn't smell like fireworks when cut and taste like acrid chalk.
If I had to do it all over, I'd do the Hardieboard again. But I'd probably spring for the special circular saw blade.