  We use the statistics of regions above or below a temperature threshold
(excursion sets) to study the cosmic microwave background (CMB) anisotropy in
models with primordial non-Gaussianity of the local type. By computing the
full-sky spatial distribution and clustering of pixels above/below threshold
from a large set of simulated maps with different levels of non-Gaussianity, we
find that a positive value of the dimensionless non-linearity parameter f_NL
enhances the number density of the cold CMB excursion sets along with their
clustering strength, and reduces that of the hot ones. We quantify the
robustness of this effect, which may be important to discriminate between the
simpler Gaussian hypothesis and non-Gaussian scenarios, arising either from
non-standard inflation or alternative early-universe models. The clustering of
hot and cold pixels exhibits distinct non-Gaussian signatures, particularly at
angular scales of about 75 arcmin (i.e. around the Doppler peak), which
increase linearly with f_NL. Moreover, the clustering changes strongly as a
function of the smoothing angle. We propose several statistical tests to
maximize the detection of a local primordial non-Gaussian signal, and provide
some theoretical insights within this framework, including an optimal selection
of the threshold level. We also describe a procedure which aims at minimizing
the cosmic variance effect, the main limit within this statistical framework.
