I read your reply with great interest since I, too, have had this question and would like to know the answer (s) to this effect.
My question is how does one separate out the effects of cold air downdraft (if there is such a thing, but I think it is the reason for the 'first gust' in front of a storm) from cold rain from higher up cooling the air surrounding it as it falls through, vs. the evaporative cooling you mention in your note?
Are each of these effects so distinct that there is a mechanism to detect which one is the major effect producer? Which of these (and no doubt other causative factors) is the elephant and which is the flea for the total effect?
As one who can be misled by trying to apply one circumstance, wrongly, to explain another effect, I'd like to learn more about this effect. (example of a helium filled balloon moving away from the acceleration when one goes around a corner in a car with the windows closed, seems wrong until you know the physics behind it).
To me, opening a freezer door in the grocery and feeling the cold blast is attributable to in essence a downdraft of falling cold air, perhaps pulled down by the countless, near freezing, raindrops or whatever mechanism that downdrafts may occur. Then there is the effect of the cold rain chilling the air at this level, and then, lastly in my way of evaluating this, would be evaporatative cooling, which isn't huge inside a storm area where the humidity is already nearly if not 100% (sorry to not talk dew points for this simplistic approach). Also knowing how poorly I cool with evaporation when its hot and humid, and how poorly the evaporative coolers work for rooms when people try those instead of usual air conditioning, would make me think this would be a lessor effect.
Those graphs show a sizable shift in pressures and it would be interesting to see what a very sensitive barometer might show during the approach of a single cell, with the first gust hitting the instrument, then when rain started, noting the temperature of the rain and changes in the surrounding air temperature, but then somehow gathering similar data at each 1000' altitude (tough during a storm!) to see what these all are showing for an interplay.
As a pilot who would avoid storms of any sort, I know from ground school and practicality that there are multiple factors and what seems logical doesn't at all prove to be the major factor in many situations, so I'm intrigued by your bringing in this condition that I'd never even considered.
Rest assured that despite my devil's-advocate approach to this, that I'm all ears and very excited to learn something new so please don't take this as a one sided criticism, I'm hoping you can help us discover other facts about storms, with all their intrigue and excitement as to how they work.