We propose a scheme to simulate lattice spin models based on strong and long-range interacting Rydberg atoms stored in a large-spacing array of magnetic microtraps. Each spin is encoded in a collective spin state involving a single nP Rydberg atom excited from an ensemble of ground-state alkali atoms prepared via Rydberg blockade. After the excitation laser is switched off the Rydberg spin states on neighbouring lattice sites interact via general isotropic or anisotropic spin-spin interactions. To read out the collective spin states we propose a single Rydberg atom triggered avalanche scheme in which the presence of a single Rydberg atom conditionally transfers a large number of ground-state atoms in the trap to an untrapped state which can be readily detected by site-resolved absorption imaging. Such a quantum simulator should allow the study of quantum spin systems in almost arbitrary two-dimensional configurations. This paves the way towards engineering exotic spin models, such as spin models based on triangular-symmetry lattices which can give rise to frustrated-spin magnetism.