Always best to quantify what the actual water temps and light penetration are when speaking of "cold and muddy." I find that bigger bass feed very well in off-colored waters from 50 down to around 42 degrees. By off colored, I mean that I can see a white bait down 18 inches-2 feet. Normally this body of water has 6 foot plus visibility. So getting the water quite stained and quite cool means lunker time for us. Small fish rarely bite then, so ten bites often equals 30 lbs. of bass. And yes, they are shallow by rule. Jigs.
Yesterday, at Lake of the Ozarks, the finals of the OMTT tournament weighed in massive stringers mostly caught on spinnerbait and buzzbait in the 55 degree water. These fish were hugging the banks. The big hickory shad were there too. Aha! Ait temps ranged in the high 30's and low 40's. Not to worry.