  We investigate the zero-temperature glassy transitions in the square-lattice
+- J Ising model, with bond distribution $P(J_{xy}) = p \delta(J_{xy} - J) +
(1-p) \delta(J_{xy} + J)$; p=1 and p=1/2 correspond to the pure Ising model and
to the Ising spin glass with symmetric bimodal distribution, respectively. We
present finite-temperature Monte Carlo simulations at p=4/5, which is close to
the low-temperature paramagnetic-ferromagnetic transition line located at
p=0.89, and at p=1/2. Their comparison provides a strong evidence that the
glassy critical behavior that occurs for $1-p_0<p<p_0$, $p_0=0.897$, is
universal, i.e., independent of p. Moreover, we show that glassy and magnetic
modes are not coupled at the multicritical zero-temperature point where the
paramagnetic-ferromagnetic transition line and the T=0 glassy transition line
meet. On the theoretical side we discuss the validity of finite-size scaling in
glassy systems with a zero-temperature transition and a discrete Hamiltonian
spectrum. Because of a freezing phenomenon which occurs in a finite volume at
sufficiently low temperatures, the standard finite-size scaling limit in terms
of $TL^{1/\nu}$ does not exist: the renormalization-group invariant quantity
$\xi/L$ should be used instead as basic variable.
