The effect will have no direct relation to your S.P.E.C.I.A.L or skills apparently.
With that in mind I would think maybe something like a little extra rad resistance? Maybe a purely aesthetic effect? Maybe by "effect" they worded it poorly & meant collecting snow globes is just for the sake of collecting?
"Funny thing about being a game designer, there's 5 million people who think they know my job better than I do." ~Demize99