The most recent LHR forecast (TAF) is only looking as far ahead as Friday noon and at the moment is showing a lowish probabilty of snow, however as you can probably see the BBC forecast is from snow right through from Friday Noon onwards through all day Saturday.
As Dave has pointed out there's definitely lots of new kit at LHR but pretty much "untested in action", so to speak, so I'm not sure of the "confidence level".
Personally if I really had to connect with an important onwards flight I'd get to LHR as soon as practical (and to give some idea of my confidence level I'm travelling to LHR later today to "connect"
for a Fri PM flight, FWIW).
Needless to say your call; good luck, and if you do go for an early flight option and then end up killing time watching the sun shine at LHR feel free to blame me .