Is it only an analogy? Similar to saying that the Higgs boson is like glass that slows down light and, thereby, seems to give it "mass"? I've looked up a little about ferromagnetism and potential energy isn't mentioned explicitly. I think I have a decent understanding of the Standard Model but I know nearly nothing about ferromagnetism (or the Ising model, paramagnetism, etc).
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Spontaneous symmetry breaking isn't defined to refer only to what the Higgs field does; it's a much more general phenomenon, of which ferromagnetism is an example. In fact, both examples result from the need to specify one vector of a given modulus. For Higgs, SSB amounts to choosing a complex scalar's phase, or equivalently an arbitrary direction in $\Bbb R^2$. For ferromagnetism, it happens in $\Bbb R^3$ instead, but the principle is otherwise the same.
