As you know there are 4 seasons in the mid-latitudes that encompass 3 months each: Winter, Spring, Summer, and Fall. The seasons are currently based purely on where the sun's perpendicular (perp.) rays strike the earth. Winter (perp. Rays moving from 23.5 S to equator), Spring (perp. Rays moving from the equator to 23.5 N), Summer (perp. Rays moving from 23.5 N to equator) and Fall (perp. Rays moving from equator to 23.5 S).
This gives us 4 almost perfect equal time periods and thus 4 seasons. How do the climatological temperature patterns follow the four seasons? The temperatures are pretty much the same when comparing early winter to late winter and pretty much the same when comparing early summer to late summer. However, late Fall is much colder than early Fall and late Spring is much warmer than early Spring. Why is that? The reason is linked to the changing of the solar sun angle during each season. In the Fall, the sun angle is always getting lower and in the Spring it is always getting higher. From this it would make sense that late Fall is much colder than early Fall and late Spring is much warmer than early Spring.
In the winter, the sun angle is INCREASING and in the summer the sun angle is DECREASING. This fact causes temperatures to be pretty much the same when comparing early winter to late winter and pretty much the same when comparing early summer to late summer. The cumulative cooling of the ground and ocean is partially offset by an increasing sun angle in the winter and the cumulative warming of the ground and ocean is partially offset by a decreasing sun angle in the summer. This causes the Spring and Fall seasons to seem much quicker in duration than the Summer and Winter seasons. The sun angle changes much more quickly through the equinoxes than through the solstices.
One idea for mid-latitude seasons would be to have the following season structure: Summer: June through September (4 months), Fall: October and November (2 months), Winter: December through March (4 months) and Spring: April and May (2 months). This season structure would fit the temperature patterns more closely. The mid-latitudes tend to have long summers and long winters with a quick temperature change during Fall and Spring. The notion of seasons is a "human construct" that tries to fit reality in some way. The season structure now in place could be changed with respect to the mid-latitudes to mirror reality more closely.