I've only every experienced carb icing once. The engine didn't stop firing - it just coughed and spluttered a bit.
Maybe you were unlucky enough to have a bit of ice the right size and shape to block the carb. At 300', you have a lot going on in your head, but, did you put carb heat on? Was there a slightly higher than normal RPM reading (assuming you were on full power on the climb out) if you did? How long was the carb heat on for before you closed it on short final?
Maybe if you could describe the engine characteristics leading up to and after the event in a bit more detail, maybe those more technically minded than me could make an educated guess.
Would air in the fuel line cause this?
Edit: previous 2 posts made as I was typing this. I echo Gertrude's sentiments.