What are the consequences in high-energy of the non-interaction of the Higgs Field? At high-energies when the Higgs field won't affect (interact with) particles, when the symmetry breaking won't occur, what would be $\rm W\pm$ or $\rm Z^{0}$ bosons speed if they would then have a $0$ rest mass? What about Fermions?
 A: In the unbroken phase of the Standard Model, all particles are massless. Thus, they can only move with the speed of light, in order to fulfill the mass-energy-relation
$$ E^2 = \vec p^2 c^2  + m^2 c^4 = \vec p^2 c^2 \big|_{m = 0} $$
This is true for photons and gluons in our broken world, but would be true for $W^\pm, Z^0$ (or more correctly for the $W^{i}, B$ bosons of $SU(2) \times U(1)$ as there would be no need to form linear combinations of them) and for all fermions as well.
A: Originally, you have 3 massless gauge bosons $W_x, W_y, W_z$ for the symmetry $SU(2)_L$ and one massless gauge boson $X$ for the symmetry $U(1)_Y$.
With the higgs mechanism, you have linear combinations of $W_z$ and $X$ which give the massless photon and the massive $Z_0$, while the $W \pm = W_x \pm iW_y$ acquire a mass, too.
So, all these particles : photon, $Z_0, W \pm$, are not the original massless gauge photons of $SU(2)_L$ and  $U(1)_Y$.
While the mass of the photon is always zero, even at high energy, there is, of course, a variation of the mass of the  $Z_0, W \pm$, due to the  energy scale (all masses of massive particles depend on the energy scale, like coupling constants). 
