  We consider $f(T)$ gravity for a Weitzenbock spherically symmetric and static
spacetime, where the metric is projected in the tangent space to the manifold
for a set of non-diagonal tetrads. The matter content is coupled through the
energy momentum tensor of an anisotropic fluid, generating various classes of
new black hole and wormhole solutions. One of these classes is that of cold
black holes. We also perform the reconstruction scheme of the algebraic
function $f(T)$ for two cases where the radial pressure is proportional to
$f(T)$ and its first derivative.
