The squashing and stretching in cartoons are not arbitrary, but derived largely from physical laws to accentuate pushing and pulling forces. Thus the mass and weight distribution of a character greatly effects how an animator should choose to squash and stretch the character's limbs.
I studied the center of mass of Mickey's walk and the walk of a human mimicking Mickey's walk.

I took a walk sequence from the cartoon "Orphan's Benefit" (1941).

I extracted a 3D approximation of the motion by rotoscoping every frame, deforming the skeleton as needed to fit the image. By assuming density in the volume of Mickey's body (27.67 kg/ft^3 - human body density) and assuming that Mickey is approximately 1 meter tall in real life, I approximated the following masses.

head = 21.304 kg
ears = 2.771 kg
thorax = 4.091
root = 7.069
arms = 4.022 kg
hands = 1.403 kg
legs = 4.241 kg
feet = 5.292 kg

Using these figures, here is the center of mass for Mickey over one walk cycle.

We captured the motion of an actor reenacting Mickey's walk. Using the following approximations for weight distributions (obtained from "Adapting Simulated Behaviors For New Characters", Hodgins and Pollard, 1997), the center of mass coordinates were found.

head = 4.22 kg
thorax = 17.62 kg
root = 11.08 kg
leg = 8.32 kg
arm = 2.51 kg

1.
The center of mass of the cartoon and the human are not identical, but they both show two major peaks, with the first one around the same time (looking at time vs. y coordinate), which correspond to the time when one foot is supporting the body and the other is in the air and at the max height that it will reach.

2.
The smaller peaks in the human COM data marks the time when a foot has made contact with the ground and the body rocks over the support that that leg provides. The small peaks are caused by force from the ground. We do not see this in the cartoon data, instead the two primary peaks are exaggerated. Where there would have been a smaller peak there is a greater depression of the COM instead.

3.
The motion capture data is a lot smoother and appears more periodic while the keyframed sequence of Mickey has more lumps and bumps. I attribute that to the keyframing process in which I extrapolated 3D position information from 2D images.

4.
The human center of mass during walk cycles is almost always a little bit in front of the root, while Mickey's center of mass tends to be higher and behind the spine.

Center of mass of the seems like seems to be a good place to find where the primary motion is. It captures the general direction of the body. Running a filter on the COM data to single out and exaggerate the major peaks should give us a COM pattern to aim for.