How much you'll need will depend on how big you want/ need it to be, and how thick you want it. A felted mattress should be a great summer project. I've not attempted anything so large as that, but I've done enough wet felting to know how I personally would begin - and summer is when I'd begin. But, you'll need to at least clean it, because, well... raw wool is rather aromatic, and likely full of bugs and debris. Then, card the fiber into bats (essentially sheets of fluffy fiber, small enough to handle, with the fibers all running the same direction), to prevent it from being lumpy.
I would find a flat sheet for the size bed I'd want, and spread it out flat, on the ground, in the shade (so you're cooler, and the water doesn't evaporate too quickly). I'd then lay the bats out in at least three 1" light, fluffy layers. In each layer, the fiber should all be running the same direction, but the next layer should run perpendicular to the one before it. So, if the fibers in your first layer run north/ south, the next layer should run east/ west, and so on. The next thing would be to spray it down with hot, soapy water, and gently walk around on it, barefoot, until the fibers mat together enough to hold onto one another. Depending on the size of the mattress, this could take a few hours, just to ensure it all clings, well. Then, I'd rinse all the soapy water from it, walk on it a bit more, to try to squeeze as much water out as possible, and drag it (still on the sheet) into the sun to dry.
If you're going to make it very thick, it might be best to make several of these, then tie-quilt them together (basically just tieing a heavy thread through what will temporarily be the blankets, about every 10") for easier management, until you have it the thickness you want. Other advantages to doing this in several blankets is that it will dry faster, than all in one large go, plus, if you change your mind, you'll still have some nice warm blankets to use &/or gift!