  We consider quantum Hall states at even-denominator filling fractions,
especially $\nu=5/2$, in the limit of small Zeeman energy. Assuming that a
paired quantum Hall state forms, we study spin ordering and its interplay with
pairing. We give numerical evidence that at $\nu = 5/2$ an incompressible
ground state will exhibit spontaneous ferromagnetism. The Ginzburg-Landau
theory for the spin degrees of freedom of paired Hall states is a perturbed
CP$^2$ model. We compute the coefficients in the Ginzburg-Landau theory by a
BCS-Stoner mean field theory for coexisting order parameters, and show that
even if repulsion is smaller than that required for a Stoner instability,
ferromagnetic fluctuations can induce a partially or fully polarized
superconducting state.
