Here you are describing the condensing coil which is normally the outdoor or backroom part on a air conditioner
After the compressor, the discharge line carries High Temperature high Pressure gas to the condensing coil to reject heat and cause state change in the refrigerant. a Low Temperature high pressure Liquid.
Here you are describing the metering device which is the divide between the High pressure side and low pressure side of the system and feeds the evaporator . This drop in pressure starts a state change in the refrigerant. now to change state the refrigerant required a huge amount of energy and to get this energy from absorbing heat from the surrounding area (this includes the pipework).
This is what is happening here. The tool and the end of the hose becomes an evaporator absording heat.
The air is actually Absorbing heat to cause this issue. The air will move slower near inside walls of the pipe, this slower move air may start to have its water vapour condense even freeze against the insides of the pipe (really there should not be this much water vapour in the compressed air by the time it reaches the tool…). meanwhile the air flow (laminar ) in the middle of the pipe is still absorbing heat .
This effect is exploited by vortex and membrane air coolers at the expense of a huge pressure drop and/or the blowing off some of compressed air to atmosphere.
@Sticks This is a topic from awhile that discusses some of these coolers
IMO the kind of heat exchanges we want for rejecting heat from compressed air are condensing coils, that reject heat and maintain pressure.