One engine can supply air to both packs, but it doesnt matter on the ground. One pack or no packs is sufficient for taxi in.
Wing antice is not used on the ground.
Engine antice is, but only on a running engine.
In freezing fog etc, the engine is not run up during taxy in. The aircraft arrives on the gate with ice on the fan blades which is removed by the ground crew.
Modern engines only have the cowl deiced. The fan blades and spinner are deicied by centripetal force. This does not work below 70%N1.
So after taxying out in freezing fog you must run up the engine to remove the ice before departure. Even this does not always work. Ask SAS about Oslo airport 3 years ago when they failed 3 B737 CFM56 engines the same day in freezing fog.
The RR Trent engine is very susceptible to freezing fog and the core of the engine can ice up. This will stop you as the only real way to remove it is to park the aircraft in the hangar for a while!