but before touch down (approx 100 feet) carb heat MUST be set to COLD. The reason for this is simples = if you are forced to do a go around, full engine output will be required to ascend,
If the carb heat
must be set to cold before landing, the aircraft flight manual will state this. The aircraft flight manual is the
only "official source" of procedural information about the operation of the aircraft systems. It would not be an error to operate an aircraft in accordance with the procedures stated in the flight manual - in fact, it is expected with good airmanship! The selection of flight manuals I have here generally say "carb heat to cold
after landing", though one flight manual I have says: "The approach technique is as follows....and carburettor heat off [cold] unless carburettor icing conditions prevail". I have never seen an instruction in a flight manual to reselect carb heat to cold on short final approach.
If, the pilot decides to overshoot, the carb heat can be moved to the cold position quickly - in many aircraft, without removing one's hand from the throttle. Certainly easily in any aircraft, and without detracting from the ability of the pilot to safely control the aircraft on climbout. A pilot who's workload is too high when having to select carb heat cold at the time of the decision to overshoot, is perhaps flying beyond their skill. It gets a lot more busy when you're flying a multi, and having to reconfigure flaps, cowl flaps, trim, and get the gear up after positive rate - carb heat is nothing compared to all of that!
The aircraft will safely climb with the carb heat hot, if all other things as they should be. Certainly at least enough climb to begin the overshoot, and get the aircraft reconfigured. If you think about it, the application of carb heat generally reduces the RPM (for fixed pitch prop engines) about 100 or so. Can you takeoff and climb away a C 150 at 2400RPM instead of 2500+? Of course you can. It's going to take more space, but is safely possible in most normal dimension runways. For the C 150, takeoff and climb away is possible at engine speeds as slow as 2100 RPM - though it's going to take a lot more runway and clearway. If you're going into a runway from which you cannot safely overshoot carb heat hot, you have already committed yourself to a landing from which a safe overshoot is not possible - and there are some, so it happens.