Does a crystalline ferromagnetic solid break the rotational symmetry twice? Both Heisenberg ferromagnets and crystalline solids break the rotational symmetry in space. Now consider a crystalline ferromagnetic solid. By virtue of being in a crystalline phase, it already broke the rotational symmetry. Having broken that, how can it further break the rotational symmetry which is already broken (by achieving a ferromagnetic order)? Also, why should that have additional consequences?
 A: It seems like you are confusing spatial rotation symmetry and spin rotation symmetry. They are different symmetries (and both are present in nature).
In terms of group theory we will say that spin rotation symmetry is manifested by invariance of the hamiltonian with respect to group $SU(N)_{\text{spin}}$ where $N=2S+1$. Spatial symmetry by $SO(3)_{\text{space}}$. If you have both independently then the hamiltonian is invariant with respect to $SU(N)_{\text{spin}} \times SO(3)_{\text{space}}$, any combination of the two. You can also have the hamiltonian be invariant to $SO(3)_{\text{spin,space}}$. This is a subgroup of $SU(N)_{\text{spin}} \times SO(3)_{\text{space}}$, in which rotations are taken simultaneously in space and spin space. Now most systems are symmetric with respect to $SU(N)_{\text{spin}} \times SO(3)_{\text{space}}$, however the action of physically doing a rotation corresponds to $SO(3)_{\text{spin,space}}$. This is one reason to be confused. Pure spin rotation ($SU(N)_{\text{spin}}$) can be obtained with magnetic fields.
Now we will say that a system breaks a symmetry spontaneously if the observed ground state is not symmetric with respect to a given group although the hamiltonian is. Ferromagnetic systems spontaneously break $SU(N)_{\text{spin}}$ symmetry and crystals $SO(3)_{\text{space}}$ symmetry. So, to answer your question, they do not break the same symmetry. A ferromagnetic crystal will break both.
They also break $SO(3)_{\text{spin,space}}$ although it is not necessarily the case that when the first two are broken, this last will be broken. You could imagine a system in which the spin rotation symmetry breaking perfectly compensates the spatial rotation symmetry breaking.
A: No, it does not. A symmetry is either broken or unbroken. Breaking the symmetry twice does not make any sense.
The ferromagnetic phase would in general break additional rotational symmetry. 
In other words, while it is true that the crystal breaks the rotational symmetry for all rotation angles around any axis, it preserves in general rotational symmetry for discrete angles around some axes. Then the ferromagnetic phase would break one or more of the remaining crystal symmetries.
For example, a cubic crystal is still symmetric for rotations of $\pi/2$ around the cubic axes. If now you have a ferromagnetic phase with spins polarized along the $z$ axis, you see that rotational symmetries around the $x$ and $y$ axes have been broken.
