In fairness, the BA examples which were given in a previous post were where a departing aircraft was at the gate and the passengers weren't given the opportunity to disembark during a long delay, as required by the regulations. Somewhat different from the situation described by the OP where the aircraft apparently couldn't even get to the terminal. The OP has said that a gate had apparently been forecast by the EWR controllers to be available within the 4 hr deadline, so it was hardly BA's fault if that was then removed at the last minute.
The problem with all these creeping delay situations where the resolution is outside the carrier's control is that the crew and ops department simply don't know how long the delay is going to be except with benefit of hindsight. The issue perhaps is whether BA had any option to disembark in the half hour window once the promised gate had been withdrawn, which would have met the 4hr deadline. I doubt whether at that stage a taxiway disembarkation in a snowstorm could have been quickly arranged, or indeed a safer and better option for the passengers, given the limited chances of getting baggage off as well amidst the chaos. Did BA then make all reasonable efforts to keep the passengers safe, watered & informed during the delay - the OP seems to accept that they did.
These things do occasionally happen if the tight choreography of stand planning at a busy airport already at limits on a normal day faces a situation where it has all the arrivals but no few or no departures - as we saw in extremis on 9/11,the alternative is closing the airspace and sending diversions all over the continent. It's terribly frustrating, but just occasionally in life it quite possibly isn't BA's fault!