Nope! SNOOZ is engineered so the energy goes into producing sound and not moving air, so the inflow and outflow are close to zero. As a result of this design, dust, pet hair, and anything else are not filtered through the device like a common fan.
Depending on your sleep environment, it is possible that a slight amount of dust may show on the fabric over a long period of time, but it is easily brushed off and should not be a major nuisance.
To clean the non-fabric surfaces, turn off and unplug the unit. Gently wipe down the surface with a damp paper towel or soft cloth and then wipe down with a clean, dry towel. Ensure all surfaces are completely dry before plugging the unit back in and turning it on.
To clean the power cord, turn off and unplug the unit. Wipe down the cord with a dry towel only.