  Various noncollinear spin textures and magnetic phases have been predicted in
twisted two-dimensional CrI$_3$ due to competing ferromagnetic (FM) and
antiferromagnetic (AFM) interlayer exchange from moir\'e stacking - with
potential spintronic applications even when the underlying material possesses a
negligible Dzyaloshinskii-Moriya or dipole-dipole interaction. Recent
measurements have shown evidence of coexisting FM and AFM layer order in
small-twist-angle CrI$_3$ bilayers and double bilayers. Yet, the nature of the
magnetic textures remains unresolved and possibilities for their manipulation
and electrical readout are unexplored. Here, we use tunneling magnetoresistance
to investigate the collective spin states of twisted double-bilayer CrI$_3$
under both out-of-plane and in-plane magnetic fields together with detailed
micromagnetic simulations of domain dynamics based on magnetic circular
dichroism. Our results capture hysteretic and anisotropic field evolutions of
the magnetic states and we further uncover two distinct non-volatile spin
textures (out-of-plane and in-plane domains) at $\approx$ 1{\deg} twist angle,
with a different global tunneling resistance that can be switched by magnetic
field.
