Many explanations have been proposed for the function(s) of the POFs. In Equus at least, one possible cause (not "function") is the "caveing-in" of the malar region when it is no more "sustained" by cheek teeth because they are too worn.
As example, here is the skull of an E. caballus found (...) >suite
The Hipparion of the Vallesian of Höwenegg was described in an exhaustive monography by Bernor et al., 1997. There are several more or less complete skeletons (here, the data on associated phalanges 1, 2, and 3 are grouped in the same table). My personal data are very scarce.
BERNOR, R.L., (...) >continue
Le matériel d’Orignac photographié ici appartient aux collections du Museum d’Histoire Naturelle de Toulouse. D’après Duranthon (comm. pers. 1994), Orignac se place dans la zone MN 10. Les dents jugales supérieures ne proviennent peut-être pas d’Orignac.
The material of Orignac illustrated here is (...) >suite
The material from Mont Lubéron is not homogeneous. It is also often broken and distorted. Together with the predominant Hipparion prostylum (Gervais, 1849, 1859) there are fossils of smaller and larger hiparions (Zouhri & Bensalmia 2005).
The data given here correspond only to the part of (...) >continue