All through my beekeeping career I have always questioned the established pattern (as I believe we all should). I take nothing for granted and usually conduct a great deal of research (both literature and practical) before I adopt one method or another.
As British Standard Hives are square in construction they will fit over the floor with the frames either perpendicular to the entrance or parallel to it. The "Cold Way" is the perpendicular version. In the past I have tried both ways to see what would happen, but I could not originally discern any benefit one way or the other. I adopted "Cold Way" for my standard as it suited my method of working (standing at one or other of the rear corners).
I was acquainted with a gentleman (alas now long dead) by the name of Beo Cooper. He was a Naturalist and the founder of Village Bee Breeders Association (the forerunner of BIBBA). He was a staunch supporter of "Warm Way" and I now subscribe to the same ideas myself. Everything comes round full circle, but my reasons are similar to his. I am now in favour of regressed native bees that are different in several respects to the run of the mill mongrels that abound in the UK. They have physically smaller colonies and are individually longer lived than other types of bee which means they can survive with a smaller population (hence the small brood chamber of the British Standard hive).
As each colony is less in bee numbers they are at a small disadvantage in a robbing situation, particularly against Italian crossed bees. By adopting "Warm Way" combs we give our smaller number of bees a more defendable front door.
With the frames set "Cold Way" a winter cluster will tend to progress across a set of 11 frames starting from the centre and moving to one side. This causes a problem when they get to the side wall. The cluster is then as far as it can be from the remaining stores. This can result in "isolation starvation" as they will not be able to leave the cluster, due to cold, to travel the few inches to obtain the rest of the stores.
This problem can be avoided by having the bees the "Warm Way". As they generally place their stores at the back of the hive and work their way from the front to the back as winter progresses.
One advantage of "Warm Way" is that combs are completed more fully to fill the frame right down to the bottom bar and without rounded corners.
Many of the above reasons are not applicable to Langstroth hives or American bees... The Langstroth hives only contain 10 frames, the footprint is rectangular rather than square and the bees themselves have larger colonies and are of types that are based on Italian or Carniolan genes which tend to have brood chambers consisting of more than one box.