I read an article written by William Mortensen in which he discusses the process.
I read most of William Mortensen's books and I highly recommend them to any film photographer. Mortensen had his own system that covered all stages of the process: choosing the subject, lighting, exposing, developing, printing, and finally, presenting the images. He mentioned many times that using just part of the system would most likely produce disastrous results. That includes developing to completion, so be careful.
I've a very faint idea how, but without understanding the cause and effect
As for cold development, there is a claim that it results in lower fog levels. I never had a chance to test it. That said, my default approach to processing Kodak Verichrome is HC-110(B) at about 6 degrees Celsius. The development time is around 10 - 12 minutes with normal agitation. (This is for orthochromatic Verichrome that pre-dates Verichrome Pan.) For fixing you have the option of stopping the development and gradually bringing the film to room temperature using several water baths with increasing temperature, or fix at low temperature extending the fixing time accordingly. Your final wash has to be extended as well. A snip test will tell you clearing time at low temperature, extend it twice and you will be good to go. I prefer the second option. I put the chemistry and the tank loaded with film (dry) into a water bath inside a small insulated container with the lid open in the fridge overnight to get to the target temperature. You can use double gloves (cotton inside rubber) to reduce heat transfer from your hands while agitating.
The reason why cold development could work must be complicated. There is an interplay of a single developing agent activity vs. temperature, super-additivity (when using two or more agents) and pH shift.
Another (unverified) claim is that active developers and short development times work better for expired film.
Kodak Verichrome type 127, develop before February 1946, developed in April 2022; HC-110(B), 11 minutes at 6 degrees Celsius.