Nuclear magnetic relaxation time measurements are well suited to monitor orientational and positional fluctuations of water molecules in solutions. Hence the dependence of deuteron spin-lattice relaxation rates on pressure (pless-than-or-equals, slant225 MPa), temperature (180less-than-or-equals, slantTless-than-or-equals, slant283 K) and composition (NaCl: cless-than-or-equals, slant5 m, NaI: cless-than-or-equals, slant9.5 m) are reported in undercooled NaCl/D2O and NaI/D2O solutions over wide ranges of the external variables. The anomalous increase of molecular mobility upon compression, observed in neat undercooled water becomes less pronounced with increasing salt concentration until the pressure dependence reverts to normal behaviour at the edge of the glass forming composition range. This behaviour is qualitatively different from the recently studied systems LiCl- and MgCl2-D2O. In the presence of network breaking agents like hydrostatic pressure and/or ionic solutes molecular motions can be slowed down upon cooling sufficiently for the relaxation rates to exhibit a maximum and to become frequency dependent. Within a recently developed motional model a detailed account of orientational fluctuations of water molecules can be given and conclusions are drawn regarding the influence of structure and composition on molecular motions.