It's a little tricky to tell if it's plugged internally when it's obviously plugged externally also. A temp gun is the best tool to see what the temperatures are of the air in front and behind the radiator, and the top and bottom of the radiator, thermostat housing and water pump usually. If you can get the outside clean then a very plugged radiator will have a big difference between the inlet and outlet temps, just like if the thermostat is closed/blocked. Nige has said that cores can have buildup that blocks heat flow without blocking the flow of coolant through the core, causing LOW temp difference, that's bigger radiators than I deal with and probably different contaminants too. If you know the history of the machine it's pretty easy to guess the shape of the inside of the radiator, has it ever had tap water added to the radiator, and has the coolant been tested/changed on schedule?
Hot water and dawn dish soap helps to loosen the oily mud. Or diesel if it's more greasy than muddy. Sometimes an O-ring pick and patience is the only way to get them clean.