[Abridged] We present maps of the main cooling lines of the neutral atomic gas ([OI] at 63 and 145 micron and [CII] at 158 micron) and in the [OIII] 88 micron line of the starburst galaxy M82, carried out with the PACS spectrometer on board the Herschel satellite. By applying PDR modeling we derive maps of the main ISM physical parameters, including the [CII] optical depth, at unprecedented spatial resolution (~300 pc). We can clearly kinematically separate the disk from the outflow in all lines. The [CII] and [OI] distributions are consistent with PDR emission both in the disk and in the outflow. Surprisingly, in the outflow, the atomic and the ionized gas traced by the [OIII] line both have a deprojected velocity of ~75 km/s, very similar to the average velocity of the outflowing cold molecular gas (~ 100 km/s) and several times smaller than the outflowing material detected in Halpha (~ 600 km/s). This suggests that the cold molecular and neutral atomic gas and the ionized gas traced by the [OIII] 88 micron line are dynamically coupled to each other but decoupled from the Halpha emitting gas. We propose a scenario where cold clouds from the disk are entrained into the outflow by the winds where they likely evaporate, surviving as small, fairly dense cloudlets (n_H\sim 500-1000 cm^-3, G_0\sim 500- 1000, T_gas\sim300 K). We show that the UV photons provided by the starburst are sufficient to excite the PDR shells around the molecular cores. The mass of the neutral atomic gas in the outflow is \gtrsim 5-12x 10^7 M_sun to be compared with that of the molecular gas (3.3 x 10^8 M_sun) and of the Halpha emitting gas (5.8 x 10^6 M_sun). The mass loading factor, (dM/dt)/SFR, of the molecular plus neutral atomic gas in the outflow is ~ 2. Energy and momentum driven outflow models can explain the data equally well, if all the outflowing gas components are taken into account.