Edit: I freeze my lyophilized GHRP-6 and GRF(1-29). They are not GH though, but GRF is a fairly complex protein.
"How to store Nutropin
Nutropin must be refrigerated at 2–8°C/36–46° before (powder form) and after (liquid form) reconstitution. Reconstituted Nutropin cannot be used after 14 days and should be discarded. Unopened vials of Bacteriostatic Water for Injection, USP (benzyl alcohol preserved), should also be refrigerated at 2–8° C/36–46°F.
It is important to protect all vials from light, including the reconstituted medication, and store them in a clean, safe place in the refrigerator when not in use."
**broken link removed**
Dat's sticky also has GH storage conditions I believe. Just search his thread.
In a nutshell, I think the cold temps are a benefit, assuming they're in lyophilized form.