I also tend to notice it if the front end is elevated (stopped on a hill for example). But I don't have enough time with the car at my new address to see if that was merely a coincidence with cold starting. I haven't noticed it more than once since we moved. The question I raise is; Has anyone noticed it with defrost on, more so than just cabin heat? I'm wondering if it could be linked to the one motor coupled to the ICE for generation purposes?
If this is the case, maybe the vibration is exacerbated by electrical load, while the generator is trying to charge the batteries. I'm willing to bet that the blower motors are tied to the 12v system, maybe it's a combination of ICE running, generator charging HV, and AGM batteries.
This is purely speculation at this point, but it comes from the thought that heater on/off has a noticeable affect on vibration.
There is also the founded theory that cold oil/cold start has an affect on engine harmonics. Unfortunately I don't have a way to data-log engine parameters to isolate things like battery charge level, fuel trims, engine temperatures etc...
Last theory is that the engine runs intentionally lean when cold to heat the catalytic converter faster. A lean fuel trim would produce more heat, and if engineered correctly, an acceptable amount of knock could be felt throughout the vehicle. I remember once upon a time reading something about the design limitations they strived to overcome in start stop ICE operation to make the Atkinson hybrid system more efficient.