  The $s=1$ spinor Bose condensate at zero temperature supports ferromagnetic
and polar phases that combine magnetic and superfluid ordering. We investigate
the formation of magnetic domains at finite temperature and magnetic field in
two dimensions in an optical trap. We study the general ground state phase
diagram of a spin-1 system and focus on a phase that has a magnetic Ising order
parameter and numerically determine the nature of the finite temperature
superfluid and magnetic phase transitions. We then study three different
dynamical models: model A, which has no conserved quantities, model F, which
has a conserved second sound mode and the Gross-Pitaevskii (GP) equation which
has a conserved density and magnetization. We find the dynamic critical
exponent to be the same for models A and F ($z=2$) but different for GP ($z
\approx 3$). Externally imposed magnetization conservation in models A and F
yields the value $z \approx 3$, which demonstrates that the only conserved
density relevant to domain formation is the magnetization density.
