We study the dynamics of water confined between hydrophobic flat surfaces at low temperature. At different pressures, we observe different behaviors that we understand in terms of the hydrogen bond dynamics. At high pressure, the formation of the open structure of the hydrogen bond network is inhibited and the surfaces can be rapidly dried (dewetted) by formation of a large cavity with decreasing temperature. At lower pressure we observe strong non-exponential behavior of the correlation function, but with no strong increase of the correlation time. This behavior can be associated, on the one hand, to the rapid ordering of the hydrogen bonds that generates heterogeneities and, on the other hand, to the lack of a single timescale as a consequence of the cooperativity in the vicinity of the liquid–liquid critical point that characterizes the phase diagram at low temperature of the water model considered here. At very low pressures, the gradual formation of the hydrogen bond network is responsible for the large increase of the correlation time and, eventually, the dynamical arrest of the system, with a strikingly different dewetting process, characterized by the formation of many small cavities.