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The structural organization of matter in poly(vinyl alcohol) (PVA) hydrogels obtained by repeatedly freezing and thawing dilute solutions of PVA in D2O is investigated by use of small-angle neutron scattering measurements (SANS). This study is the first systematic and quantitative investigation in the medium range of length scales on PVA hydrogels obtained by freezing and thawing techniques. The studied gels have a complex hierarchical structure, extending over a wide range of length scales. The structural organization on the micron length scale originates from the presence of two separated phases constituted by polymer-rich and polymer-poor regions. The network structure may be interpreted in terms of the connectivity of the regions occupied by the polymer-rich phase, which extend over the macroscopic dimensions of the sample. The organization on the medium length scale is provided by the presence of small crystallites, fringed micelle-like, within the polymer-rich phase. In these regions, the crystals are highly connected by swollen amorphous tie chains. The presence of these tie chains ensures the connectivity of the macroscopic network. The structural organization on the short length scale is essentially provided by the relative arrangement of chains within the crystallites and in the swollen amorphous zones. The PVA hydrogel structure has been modeled as a collection of polydisperse and homogeneous spherical crystallites, interacting via hard-spheres potential. SANS experiments permitted us to obtain values of the crystallite size of about 33 Angstrom, of the volume fraction of polymer-rich phase of the order of 1% and a value of the average crystallite-crystallite correlation distances of the order of a few tens of nanometers, independent of the imposed number of freeze/thaw cycles (n), for n > 1. The present analysis also indicates that the structure of the gel obtained imposing a single freeze/thaw cycle is somehow intermediate between the structure of the homogeneous starting solution and the structure of the already well-formed sample obtained by imposing two consecutive cycles.