J3 CUB HAS ENG FAILURE JUST AFTER TKOF.

Narrative

I WAS THE REAR SEAT PLT OF A J3 CUB RECEIVING TAILWHEEL TRAINING FROM A CFI. THE AIR TEMP WAS 30 DEGS F WITH AREAS OF RAIN AND SNOW IN THE VICINITY BUT NONE AT THE ARPT. A PROPER THOROUGH PREFLT INSPECTION WAS PERFORMED. AFTER THE COLD ENG WAS STARTED (HAND PROPPED) A RUN-UP WAS PERFORMED WHILE THE ACFT WAS TAXIED. TKOF ROLL WAS COMMENCED FROM A MID-RWY INTXN INTO A 15 KT DIRECT HEADWIND. BECAUSE THE ENG WAS RUNNING POORLY WITHOUT CARB HEAT; CARB HEAT WAS APPLIED DURING THE EARLY TKOF ROLL; THEN REMOVED. THE ENG RAN SMOOTHLY AND ROTATION WAS NORMAL. CLB PERFORMANCE WAS NORMAL. AT APPROX 200 FT AGL THE ENG ABRUPTLY FAILED. CARB HEAT WAS IMMEDIATELY APPLIED. THE ENG NEVER RESTARTED. THE ACFT WAS OVER THE DEP END OF THE RWY. TREES AHEAD PRECLUDED STRAIGHT AHEAD LNDG. A 180 DEG R TURN WAS MADE AND THE ACFT WAS LANDED SMOOTHLY WITHOUT DAMAGE OR INJURY IN A SNOW COVERED PLOWED FIELD PARALLEL TO THE RWY. CTL WAS MAINTAINED AND OBSTACLES AVOIDED; DESPITE THE DOWNWIND LNDG AND LACK OF OPTIONS DUE TO LOW ALT AND POOR GLIDE RATIO OF THE J3; CARB ICING CAUSED THE ENG FAILURE. CONTRIBUTING PROBS: QUICK RUN-UP WHILE TAXIING; NOT USING ENTIRE AVAILABLE RWY FOR TKOF; TIMING OF REMOVING CARB HEAT. OTHER FACTORS: GOOD FORTUNE!