Photons in vacuum have no proper time, and they are not considered as observers and not as reference frame. But what about photons travelling through matter? Their velocity is lower than light speed, thus the proper time formula (multiplication with reciprocal gamma) would yield a proper time, but do we consider that they have a proper time/ that they are observers/ that they may be reference frames?
As my answer to How do photons know they can or can't excite electrons in atoms? explains, when a photon interacts with matter it is no longer just a photon. The photon/matter system has to be described by a wavefunction that describes both and that isn't separable into a photon bit and a matter bit.
When the interaction is strong, e.g. in Bose-Einstein condensates, the interacting system is described as a quasiparticle called a polariton. For light passing through glass the interaction isn't strong enough for this to be a useful description, but the idea remains the same. The photon/solid system now has a mass and propagates at less than $c$, so it does have a non-zero proper time.