Skyrmions are promising for the next generation of spintronic and magnonic devices, but their zero-field stability and controlled nucleation through chiral interactions remain challenging. In this theoretical study, we explore the potential of moir\'e magnetic heterostructures to generate ordered skyrmion lattices from the stacking-dependent magnetism in 2D magnets. We consider heterostructures formed by twisting ultrathin CrBr_3 films on top of CrI_3 substrates, assuming a moderate interfacial Dzyaloshinskii-Moriya interaction. At large moir\'e periodicity and appropriate substrate thickness, a moir\'e skyrmion lattice emerges in the interfacial CrBr_3 layer due to the weaker exchange interactions in CrBr_3 compared to CrI_3. This lattice is then projected to the remaining layers of the CrBr_3 film via emergent chiral interlayer fields. By varying the pristine stacking configurations within the ultrathin CrBr_3 film, we realize layered ferromagnetic and antiferromagnetic skyrmion lattices without the need for a permanent magnetic field. Our findings suggest the possibility of creating colorful skyrmion lattices in moir\'e magnetic heterostructures, enabling further exploration of their fundamental properties and technological relevance.