A good deal has been answered on the Chemistry portal to which Prashant directed us. But strangely, a simple aspect has been ignored ! So I will suggest the same as my two-penny bit:
Have we noticed that while the rain droplets are likely to be cold due to continuous evaporation on the way, the ground is likely to be hot (particularly in countries like where Slimane or myself are located !) ? And there is heterogeneity of temperature both ways !
That is, at some spots, air trapped in surface pores is hot enough, and the rain drop falling is simply cold enough for the bubbles to form.
It should non-linearly depend on the size, shape at the moment of impact and the speed of the droplet. The surface tension of liquid is also important. In the impact zone a bubble will originate from the impact waves and depending on the penetration depth of the droplet into the liquid there is a chance for a formation of a stable bubble. In the case of the small droplet or not deep enough penetration the chances are decreasing. But it needs additional experimental investigation.
Bubbles consist of a gas trapped by a liquid, where the liquid has a surface tension high enough to encapsulate the gas. This gives bubbles three ingredients: the liquid, the gas, and surface tension.