The best I can do is a qualitative answer. Tris buffers are less susceptible to microbial attack than, say, phosphate buffers. I recall reading somewhere that Tris is a weak uncoupler of oxidative phosphorylation, which would tend to slow down aerobic microbial growth. I don't have a citation on that issue at hand, however. For short term use, a refrigerator is probably OK, but it is important to give any buffer sufficient time to reach temperature equilibrium. For longer term storage, I would freeze, but then I would mix thoroughly when I thawed it out. Arkcon made some very good points in the linked answer.