2.0TDCI will start in this weather without glow plugs. They’ll also normally start with minimal cranking in the depths of winter without functioning glow plugs.
My initial thought was timing jumped, but the white smoke rules that out, as if the crankshaft and camshaft aren’t seen as being synchronised fuel won’t get injected.
Instead the white smoke would make me look at the fuel system. Air ingress is not likely to produce white smoke, as if there’s no fuel pressure, the injectors won’t even open, however if there’s a leaking injector it might, and also a leaking injector may prevent the fuel rail pressure from building high enough to open the injectors, but so could a few other things.
Realistically, unless you can recreate the fault with live data available to monitor the engine basics, everything is a wild guess, and you’re simply playing parts darts in the hope something fixes it.