Rajesh, in my opinion you will be doing yourself no favors by keeping STZ vial in ice bucket or trying to weigh it in a cold room because STZ is hygroscopic and once it is hydrated, the clock begins and its observed efficacy decreases, as one would expect.
Normally, you should store the powder in a freezer (-20, or lower). When you are ready to use it (or split it in portions), take the bottle out and keep it at room temp in darkness and make sure it is fully equilibrated to RT (not just the exterior but also the powder). Before opening the bottle, have multiple tubes ready (pre-weighed and labeled), add the approximate amount (minimum or greater than) you will need. Weigh, record the weight, and seal them (cryo-vials work well). Use the difference in weights to get an accurate number; do not waste time in trying weigh exactly the weight for the animal(s). When you are ready to inject, dissolve the powder by calculating the final concentration in dilute HCl or Citrate buffer such that you can inject the correct amount without having to think too hard (and waste time). For example, a 100gm rat gets 100microliter or a 20gm mouse gets 40microliter etc. Whatever proportions work well for you is fine (within a reason) but minimizing the total time from the point of dissolution to injection is one of the important points.