should pitchers ice: right after pitching?, only when their arm throbs/ hurts/feels pain?, or always after throwing even if it is a bullpen or long toss?..or would lik tubing and using light dumbell shoulder/rotator cuff exercises be better?

Ice reduces swelling by reducing blood flow. Arm recovery needs blood flow. So, unless you’ve got an injury with accompanying swelling or inflammation, there is no need to ice. Post-game cardio activities like light jogging, riding an exercise bike, etc.) increase blood flow without further taxing the arm so they help with arm recovery.

So, you should always do the cardio. Ice is optional.