An approach based on the Time-Dependent Self-Consistent Field (TDSCF) is used to carry out quantum calculations of inelastic atom scattering from large, highly anharmonic clusters. The computation is carried out for low-energy collisions of Ar with (H2O)(11), and all the vibrational modes of the cluster are included. The method treats the collider atom classically, but the dynamics of the interacting anharmonic modes of (H2O)(11) is handled quantum mechanically. The results provide insight into the collision physics of large systems having soft anharmonic modes, and into the role of quantum effects in such cases. The main findings are the following: (a) Large differences are found between quantum and classical results with regard to energy transfer into specific cluster modes. (b) Classical calculations wrongly predict efficient excitation of many stiff modes, including processes that are quantum-mechanically forbidden. (c) Single quantum excitations are the most important transitions at the collision energy used. (d) Atom-atom pair distribution functions of (H2O)(11) after the collision show insignificant differences from the corresponding precollision distribution functions. The results show that quantum calculations of collision dynamics of low-temperature anharmonic clusters are feasible, and also necessary in view of the prediction of significant quantum effects.