The Mosquito™ hotend can function without active cooling (a fan) under certain conditions, but it is advisable to use a fan when printing with PLA and other lower temperature plastics (PETG, ABS, etc). The cooling fan can be positioned on either side of the heat sink, but it must face the heat break. Meaning, airflow should be directed (“pushed”) toward the heat break, NOT pulled through it.
Now, about those certain "conditions". The Mosquito™ is extremely thermally efficient and does not require as much cooling as common hotends. The primary heat sink in the FFF process is actually the filament itself - it absorbs lots of heat as it moves into the melt zone and is extruded. Higher temperature filaments absorb more heat than lower temperature filaments like PLA or PETG. Combining this property of the filament with the Mosquito™ thermal efficiency and print jobs with low, infrequent retractions, and high flow rates equate to very little heat creep, and therefore less need for cooling airflow. Other factors that play into this equation include whether the printer has a heated chamber and whether the hotend is mounted to a conductive (metal) surface, or a plastic adapter, among other things.