Why are there clouds over the Intertropical Convergence Zone?

[Hall]

Intertropical Tropical Zone is the zone where north-east and south-east trade winds converge. This zone usually occurs over (I don’t know if “on” should be here) the equator.

In the book The Atmosphere: An Introduction to Meteorology by Lutgens and Tarbuck (13th Edition), Figure 7.9 reads

The Intertropical convergence zone (ITCZ) . This zone of low pressure and convergence is seen as a band of clouds that extends east-west slightly north of the equator.

I cannot understand why are there clouds over the ITCZ. First of all, the clouds are very small water droplets at temperature well below freezing points, that implies that coming trade winds have to have moisture in them. But here is a delicate point which I haven’t understood by reading books, and I believe only by an experienced man that I can get my bridges built up (or get them repaired), how do moist winds cause cloud formation? Here is the scenario: the wind had begun from, almost, $30^{\circ}$ latitude, picked up moisture somewhere in between and reached the equator. At the equator, it may rise up and thus relative humidity reaches its maximum level. The decrease in temperature as the air rises cause the moisture in coming trade winds to form droplets, and due to absence of any nucleui, large droplets and ice crystals are not formed. These droplets at low temperatures is what we see as clouds.

Is my explanation acceptable?

 

[Baluncore]

I think you should look at the bigger picture. The Hadley cell.
https://en.wikipedia.org/wiki/Hadley_cell

 

[DrJohn]

In a convergence one mass of air willl usually ride up the frontal edge of the other, the warm air rising over the cooler air of a cold front. Rising air cools. Moisture then forms water droplets, which form clouds.
You see this with an approaching front.