I very much doubt the wheel doors were removed by choice. From the photographs I've seen, there's a good case that early production aircraft of the first batch didn't have the wheel doors fitted yet The most published photographs are however on those early ones, usually from JG77 in October/November 1944 in Neuruppin.
Later ones commonly have, from appx. the 332 xxx production block. Pretty avarage production history stuff. BTW, they were already intended for the 109G, it was just somehow not put into production (the wheel well shape was redesigned, though), even if I can find a few 109G-6s with wheel well doors.
A few pics of 109Ks with wheel well doors, nope, you can find quite a few of them :





If you look at the pic of the 109K in the snow, it pretty much screws the 'mud-theory'.
IMHO it should be added, it adds a lot of 'K-ish' feeling to the plane, and it's just eyecandy anyway.