Does the photino in super-symmetry have a mass, Or is this different in different super symmetric models?
In purely theoretical models, SUSY may be completely unbroken in which case photinos would be massless – and all particles would have the same mass as their superpartners.
In the real world, SUSY has to be broken and a photino must consequently be massive (it is infinitely unlikely that the mass agreement will survive for any pair if SUSY is broken), otherwise a photino would be easily produced and seen. For example, a pair of massless photinos would be rather easily created in electron-positron annihilations at the LEP collider a decade ago and manifested as lots of "missing energy" (because the massless photinos would be neutral and rather weakly interacting).
In general, all superpartners must be massive – and it is assumed that all of them are more massive than their known counterparts, quite possibly much more massive (or even so massive that we will never produce them).
A photino is a neutral fermion. All the neutral fermions – photino, zino (these two may also be mixed as the bino and the neutral wino), neutral higgsinos (which includes the superpartners of the neutral Goldstone mode) – are mixing with each other and we call them "neutralinos" and write their mass as a matrix. There are four (Majorana spinors worth of) neutralinos in the Minimal Supersymmetric Standard Model so we need to consider a $4\times 4$ mass matrix for these neutralinos. The eigenstates of this matrix are the "real well-defined four species" of the neutralinos with well-defined masses (eigenvalues).
A similar mixing applies to two Dirac charginos – a unified name for charged winos and charged higgsinos.
In 2012, physicists would mostly talk about "neutralinos" and "charginos" rather than "photinos" and "winos" although those concepts are different basis vectors depicting the same basic particles, as discussed above.