Does the rain come down from the cloud?
The rain comes down from the sky, not from the cloud.
But the hot wind and the cloud will lead to the falling down of the rain.
The origin of the rain is from the water vapor;
because sun-rays fall down on the earth, so that the water of seas and rivers evaporates by the sun heat;
the vapor goes up in the sky, and the vapor particles convert into water particles because of the coldness of the atmosphere in the high altitudes,
and with the continuation of the influence of the coldness on these particles, they change into snow particles which remain scattered in the sky,
then when some of the water vapor again goes up in the sky, and a hot wind comes to drive it under these snow particles scattered in the sky,
then the heat of the wind and the vapor will melt away that snow, so it will fall down as rain.
God - be exalted said in the Quran, 30: 48
اللهُ الّذي يُرْسِلُ الرِّياحَ فَتُثِيرُ سَحاباً فَيَبْسُطُهُ في السّماءِ كَيْفَ يَشاءُ و يَجْعَلُهُ كِسَفاً فَتَرَى الوَدْقَ يَخْرُجُ مِنْ خِلالِهِ
(God is He Who looses the winds, and they stir up [and collect] clouds, which He spreads in the sky as He pleases, and makes them as [many] fragments, and you [man] see the [nearby and large] rain drops issue out of the midst of the [clouds] etc.)
The الوَدْقَ is the rain, which is nearby to the ground.
So, God -be exalted explained that the rain comes down from among or through the clouds; and it is not the cloud itself that comes down as rain; that is because the hot wind and the cloud will melt away some of the snow particles scattered high in the sky, so that they will fall down as rain, from among the cloud.
God - be exalted - said also in the Quran, 24: 34
أَ لَمْ تَرَ أنّ اللهَ يُزْجي سَحاباً ثُمَّ يُؤَلِّفُ بَيْنَهُ ثُمَّ يَجْعَلُهُ رُكاماً فَتَرَى الوَدْقَ يَخْرُجُ مِنْ خِلالِهِ
(Have you not seen how God drives the clouds, then composes them, then converts them into a heaped mass, then you see the rain issuing out of the midst of them?)
The role of the wind:
The wind stirs the seas and rivers to evaporate the water, then the water vapor will rise up, then condenses, then water droplets will form, then snow crystals will form, which will stay scattered in the sky.
The wind drives the cloud, and moves it.
God -be exalted said in the Quran, 35: 9
و اللهُ الّذي أرْسَلَ الرِّياحَ فَتُثِيرُ سَحاباً فَسُقْناهُ إلى بَلَدٍ مَيِّتٍ فَأَحْيَيْنا بِهِ الأرْضَ بَعْدَ مَوْتِها
(God is He Who looses the winds, and they stir up [and collect] clouds, which We drive to a desolate [: dead] land, and thereby quicken the land, after it is desolate [: dead] )
The wind fertilizes [and impregnates] the cloud, by means of the condensation nuclei [because of the dust and smoke particles that the wind carries], and leads to formation of the cloud.
This is in the Quran 15: 22
وَأَرْسَلْنَا الرِّيَاحَ لَوَاقِحَ فَأَنزَلْنَا مِنَ السَّمَاء مَاء
(And We send forth the 'impregnating' winds, and We send down water from the sky)
The wind impregnates or fertilizes the trees; and the wind impregnates the cloud; because the wind carries some dust and smoke particles and when these collide with the snow particles scattered in the atmosphere, this will lead to warming of these snow particles causing the rain formation. [In addition, these particles will act as nuclei around which some water droplets will collect.]
Then when a hot wind and a new cloud come under the scattered snow; it will melt that scattered snow leading to the falling down of the rain.
The wind heralds the coming rain.
A cold front is the transition zone where a cold air mass is replacing the warmer air mass. The cold air is following the warm air, and is gradually moving underneath the warmer air. As the warm air is pushed upwards it will bear the cloud over it. Often the rain will fall in a few minutes as the cold front passes. As the cold front passes, the clouds roll by and you may notice that the air temperature is cooler.
This kind of cold air just before the rain is "a bearer of glad tidings of the coming rain", i.e. such cold moist slow moving air will herald the coming rain; so that many of the people will then anticipate the imminent coming of the rain.
God - be exalted - said in the Quran, 7: 57
و هُوَ الّذي يُرْسِلُ الرِّياحَ بُشْرىً بَيْنَ يَدَيْ رَحْمَتِهِ حَتَّى إذا أَقَلَّتْ سَحاباً ثِقالاً سُقْناهُ لِبَلَدٍ مَيِّتٍ فَأنْزَلْنا بِهِ الماءَ فَأَخْرَجْنا بِهِ مِنْ كُلِّ الثّمَراتِ ...الخ
(It is He Who looses the winds bearing good-tidings before [,or heralding, the rain which is] His mercy; till, when they are charged with the heavy cloud [they bear the cloud above them], We drive it to a dead land, and therewith send down [, from the sky, rain] water, and bring forth therewith all the fruits etc.)