Is boiling point a cooling process?

"Boiling point" is the temperature at which the vapour pressure of a liquid reaches the same value as the pressure that surrounds the liquid, and thereby allows the liquid to enter the vapour phase.

So it is a temperature specific to a particular liquid; it isn't a "process".

What you may be getting mixed up with here is "evaporation". Evaporation is a process by which liquid molecules in the vicinity of a liquid/vapour surface gain energy from the bulk of the liquid, and are able to cross into the vapour phase. Unlike boiling, this does not necessarily require a heat source (which is why wet washing dries on a washing line at temperatures well below 100 celcius).

Evaporation can be a cooling process, as energy is extracted from the bulk liquid or from the surrounding air by the surface liquid molecules. Because they have extracted energy, the remaining liquid, and any solid surface in contact with it, cools a little.

So evaporation can involve a cooling process, but not boiling. And boiling point is not a process but a characteristic temperature.