Despite you pointing the finger at the ECM I thought I'd throw this up just for another option.
I had very similar issues.
Hard crank, cold made it worse, rough idle, stalling.
It was an ECM relay located on the IPDM.
Dealer will want to replace the whole IPDM, they consider it a non-serviceable item even though relays and fuses pop right off the board.
On our Frontiers the ECM relay and foglight relay can be swapped in under 5 minutes to see if that fixes it.
The bad ECM relay on the IPDM is known to be an "early year" issue for Frontiers, specifically 2005 and 2006 model years, but bad ECM relays have occured on years beyond those.
If the ECM relay is not properly sealed it can become corroded over time so the symptoms can come on rather gradually (hence cold whether affecting it the worse it gets).
If you swap and that fixes the issue just make sure you buy the correct relay for the ECM and don't use the foglight relay any longer than necessary.
There is a difference between the two relays and the ECM relay has a diode that prevents back surges to the ECM whereas the foglight relay does not.
I may be wrong in this diagnosis, but hey, it's a free test to see if this is the problem or not.
BTW the new relay I bought was $4.40 delivered vs. replacing the whole IPDM board at the stealership for big bucks ($300 plus from what I know).
Good luck and let us know how it turns out please, the more info shared here the more valuable this forum becomes.
Below is a (borrowed) picture of our (Frontier) IPDM and the location of the two fuses to swap.
The two on the left are the ones, pay no attention to the ignition relay highlighted.
Your IPDM block/board may look different, this is just for reference.
The IPDM (which I'm sure the OP knows by now) is located under the hood in the fuse box left side for those that don't know.