Function $W \mapsto f(W)$ is **not** convex when $n \ge 2$. 

Take for example when $n=2$ and fix $x=1$. 

If function $f(W_1,W_2)$ is convex then it must also be convex when restricted to a linear subspace. 

Restricting to $W_1 = \begin{pmatrix} u & 0 \\ 0 & 0 \end{pmatrix}$ and $W_2 = \begin{pmatrix} v & 0 \\ 0 & 0 \end{pmatrix}$ then gives $f(W_1,W_2) = u^2 v^2$, which is not convex in $(u,v)$ (this can be checked by computing its Hessian matrix).