Aims. Dust is observed in the polar regions of nearby active galactic nuclei (AGN) and it is known to contribute substantially to their mid-IR emission and to the obscuration of their UV to optical emission. We aim to carry out a statistical test to check whether this component is a common feature based on an analysis of the integrated spectral energy distributions of these composite sources. Methods. We selected a sample of 1275 broad-line AGN in the XMM-XXL field, with optical to infrared photometric data. These AGN are seen along their polar direction and we expect a maximal impact of dust located around the poles when it is present. We used X-CIGALE, which introduces a dust component to account for obscuration along the polar directions, modeled as a foreground screen, and an extinction curve that is chosen as it steepens significantly at short wavelengths or is much grayer. By comparing the results of different fits, we are able to define subsamples of sources with positive statistical evidence in favor of or against polar obscuration (if present) and described using the gray or steep extinction curve. Results. We find a similar fraction of sources with positive evidence for and against polar dust. Applying statistical corrections, we estimate that half of our sample could contain polar dust and among them, 60% exhibit a steep extinction curve and 40% a flat extinction curve; although these latter percentages are found to depend on the adopted extinction curves. The obscuration in the V -band is not found to correlate with the X-ray column density, while A V / N H ratios span a large range of values and higher dust temperatures are found with the flat, rather than with the steep extinction curve. Ignoring this polar dust component in the fit of the spectral energy distribution of these composite systems leads to an overestimation of the stellar contribution. A single fit with a polar dust component described with an SMC extinction curve efficiently overcomes this issue but it fails at identifying all the AGN with polar dust obscuration.