Is this a new problem? The icing may be an unrelated symptom.
Have you tried removing the air filter and repeat the test. An obstructed air filter could cause some of the icing.
Also, with the tractor off and cold open the fuel drain on the bottom of the carb. You should be able to see a steady stream gas that never slows. I had an obstructed fuel line in my DC that would cause it to run for a few minutes before stalling.
Good luck troubleshooting.