If it helps, the "cold" issues for me happen only when the ambient temperature is below 40 and the engine is cold. I'm just guessing, but I think it's a problem not having enough juice to power the overall electrical system.
I have a Li Shorai battery so I always have to let it warm up before it puts out enough amps to crank. When the bike start ups, idle RPM will be low and bouncing up and down. If RPM drops below 800, the bike dies.
Again, just a guess, but low rpm -> low alternator output + low output from a cold battery => engine stall. I never had this issue with my 07 919 (stock battery, no PCIII), but my 04 (PCIII + Shorai) consistently shows this issue. Pulling out the choke to keep idle up prevents the engine from dying.
2012 Yamaha Super Tenere
2001 Honda Blackbird
2007 Honda 919
49/50 visited on two wheels. 1 more to go!