Carb ice is funny sometimes. Was doing a bunch of T&Gs in a 152. As
you, Carb Heat on downwind, push it off after pushing the throttle in on
takeoff. On my 7th or 8th "GO" the engine lost power and ran rough at
about 300' and quit as I made a right 270 back to the intersecting
runway. Made the runway, got a restart after a few moments, it ran real
rough for a bit then smoothed out. Shop checked it and found nothing
wrong, we assume it was carb ice.

More likely the engine had loaded up with raw fuel. With carb
heat on, the mixture gets pretty rich, and with the throttle closed
there is very little airflow through the engine. Fuel can puddle in the
intake manifold, and upon opening the throttle all that gasoline is
sucked into the cylinders and floods them. It's worse if you shut the
carb heat off first, as the cold air reduces the vaporization of the
fuel.
Don't make long power-off glides when it's cold and with carb
heat on. Clear the engine often, and make sure it's ready to run if you
need it.

Dan