There was a very similar incident at ARN two years ago. TBL tractor towing a Finnair MD80 on an icy ramp tried to turn when going to fast. The aircraft overtook the tractor which became stuck in the fuselage side. But our tractor kept a grip on the nosewheels.
The problem with TBLs is that they are very light. There is no added mass like you get on old type tractors.
It is standard practice when using a TBL for towing to have NOBODY on board. You don't need a brake man. The only reason for having someone on board is if you need the APU running to power the nav lights at night. At LHR, BAs TBLs all have generators fitted to supply power to the aircraft. We use a van with beacons following the aircraft.
The moral of the storey is that when towing with a TBL in the winter take it easy.