wellllll....(i'll try and answer your question twards the end of my short story !!!lol)i can tell ya what i did and what experiance i have in removing and cutting the airbox lid. number 1, just cutting the airbox lid or removing it can have two different effects on your performance. when i first cut my lid i had stock reeds and one size up in jetting cause of my fmf pipe. and after i took the lid off and cut it open it actualy made me loose power instead of gain it..so i went on ebay and bought a new lid for a few dollars adn put it back on. now.......after i put in my aftermarket reeds it made my bike run allot richer, so i put the cut airbox lid back on and i made mine exactly the same way that specialized7 made his...and it ran beautiful..so my point is that just simply taking the lid off or cutting a hole in it for extra breathing isnt always gonna benefit ya unless you have the right engine work done, its kinda like rejetting, you have to experiment with it to find what works best and sometimes it takes a while...
so to answer your question about the mud...what i did with my stock airbox lid is i cut it the same way that specialized7 did his, but i went a few steps further, i made a square plat out of plastic the same size as the opening i cut in the airbox lid, then used a whole saw to drill two 3 inch holes in it, then i cut off two 1/2 inch long pieces of 3 inch pvc pipe and glued em to the top of my airbox lid so instead of a big square hole i now have two 3 inch wholes in the middle of the lid, because the two pvc pieces i cut were 1/2 long that created a 1/2 inch lip so the water didnt easly run into my box anymore...and after i was all done i took two pieces of thin(1/2 thick) sponge and cut two circles 3 inches around and stuffed em into the holes i made on the top of my box, that way if water or mud does get into it, the sponge will soak the moister up before getting into the air box, not only does it breath through the sponge it keeps it dry. if this is confusing let me know cause i could prolly do a little diy on it with some pics..that air box worked great along with the mods i had dome at the time ..before i went with cfm airbox,