RNA can be subject to self hydrolysis by its reactive 2'-OH group on its ribose sugar moiety at basic pH > 7. The hydrolysis seems to be magnesium enhanced so inclusion of EDTA to 1 mM in 10 - 20 mM Tris buffer chelates away the magnesium. Some people recommend moderately acidic buffers for RNA storage. I have never actually worked with RNA directly. You also have to watch out for RNAse which is a nasty contaminant enzyme that can survive an autoclave. RNase Inhibitor is a protein that can be used to protect your samples from RNase activity because RNase Inhibitor binds RNase with extremely high affinity preventing RNase from degrading RNA.

DNA is pretty difficult to destroy. It can be destroyed by DNAse but fortunately DNase doesn't survive an autoclave. Scientists have extracted DNA from thousand year old mummies so DNA is quite stable under extreme conditions. I have stored DNA in 10-20 mM Tris buffer (pH ~ 8) without EDTA or in autoclaved water and nothing bad has ever happened even with repeated freeze thaw cycles.

DNA can be stored at -20C and RNA probably should be stored at -80C. I don't think ice crystal formation is even an concern for RNA and DNA. The concern is enzymatic or pH or metal driven hydrolysis.