This sounds like a dribbling injector. I don't think the normal ECU cold start operation would drastically overfuel. Maybe this injector is prone to not seating perfectly in very cold conditions. It could also be an icing issue. i.e. When the fuel is released from the injector it vaporises and the latent heat is drawn from the injector tip (similar to how a refrigerator works). Water in the atmosphere freezes on the injector which disrupts the spray pattern and might prevent the injector closing fully.I did try this during my attempts to get it started. If anything I think there was too much fuel (flooded) because there was black smoke coming from the exhaust. The spark plug was also quite wet when I took it out to make sure it was working.
I can't think of a simple way to fix this but maybe someone who is used to operating in cold climates might have some ideas. As an off-the-wall experiment how about a hair dryer or a hot air gun blowing in to the air intake?