The bizarre thing is that BA are perfectly capable of organising deicing/bad weather cover at their overseas outstations through handling agents, where the various elements in my experience always manage things straightforwardly and turn up on time (St Petersburg and Helsinki being my main although not only such experiences), but are incapable of doing so at Heathrow.
We do get winter weather regularly in London. When was the last snowfall day when the BA operation ran straightforwardly ?