Before we get to the discussion at hand on how to do the project, I want to reinforce what KSSS said about how insane you have to be to mulch or mow with an open cab machine to those out there who feel that you can get away without the proper protection. I've taken whacks to my cab door with both my mulcher and brush mower with large pieces of debris that made my ears ring for several minutes. If I didn't have that door, I wouldn't be here right now as I'd have a hole in my chest that you could pass a football through. Even with a Kevlar vest, I'd still be in serious shape due to all the broken bones I would have in my body from taking a piece of debris shot off my mower or mulcher to my body.
Jacob, in terms of your project, I don't think you'd necessarily need a skidsteer mulcher for those lots. With anything less than a Supertrak machine or prime-mover mounted mulcher, those logs will be hard to tackle if they are not thoroughly rotten. Like others have suggested, take your grapple through there and clean out all the big wood. Once that is done, I don't see anything in there that wouldn't be able to be handled by a mower on a skid in a few short hours.
Any questions- feel free to shoot 'em my way.