Surprised at BA's reluctance to assist with HOTAC, but not sure of all the facts.
However to expect BA to call every passenger throughout the day when thousands would have been affected is just plain daft! You were however informed by whatever means about 4hrs before. For extended periods of time yesterday flowrates into LHR were 26 aircraft per hour - BA has no say in the matter. The fog had been forecast the previous evening, did you make any attempt to contact the company to see if operations were running normally to 'mitigate your losses' during the day?
As Topbunk says, legally it is defined as 'an act of god' and this was accepted when you purchased your ticket, in the small print.
The quote in your original post says the flight was cancelled 'for rotational reasons' this is different to your claim that it was cancelled to operate other flights. The rotational reason covers many things, one of which may be crew hours or aerodrome operating times either at zrh or somewhere else on that aircrafts/schedules rotation. Thus mitigating BA's losses due to the 'act of god'. And without knowing when the decision was made it is unfair to criticise BA as you were made aware 4 hrs before your flight left.
As you say sudden fog did not descend on LHR last night but was severly affecting all operators out of LHR.
You may well have a case with being refused hotac, but am unsure as to whether you reside close enough to LHR to not make that necessary. Especially as you were told at 1500 and the flight the company rebooked you on was the following day. Which brings us to the point BA fulfilled their part of the deal and got you to Zrh at the earliest opportunity.