  We investigate magnetic properties of quantum dot arrays of moir\'e
triangular superlattices. Starting from a reciprocal space model, we use the
projection technique to obtain maximally localized Wannier functions and
determine generalized Hubbard model parameters. The many-body Hamiltonian is
solved using the exact diagonalization method as a function of the number of
electrons in differently shaped quantum dots arrays. Finite spin polarization
is observed within a wide range of filling factors for small twist angles and
sufficiently strong interactions in most of the studied structures. The
prospect for a magnetization controlled by applying a displacement field is
presented. In the vicinity of half-filling, signatures of Nagaoka
ferromagnetism in moir\'e materials are seen, which we demonstrate by comparing
results with the corresponding on-site Hubbard model.
