Outstanding questions about the RNA world hypothesis for the emergence of life on Earth concern the stability and self-replication of prebiotic aqueous RNA. Recent experimental work has suggested that solid substrates and low temperatures could help resolve these issues. Here, we use classical molecular dynamics simulations to explore the possibility that the substrate is ice itself. We find that at -20 C, a quasi-liquid layer at the air/ice interface solvates a short (8nucleotide) RNA strand such that phosphate groups tend to anchor to specific points of the underlying crystal lattice, lengthening the strand. Hydrophobic bases, meanwhile, tend to migrate to the air/ice interface. Further, contacts between solvent water and ribose 2-OH' groups are found to occur less frequently for RNA on ice than for aqueous RNA at the same temperature; this reduces the likelihood of deprotonation of the 2-OH' and its subsequent nucleophilic attack on the phosphate diester. The implied enhanced resistance to hydrolysis, in turn, could increase opportunities for polymerization and self-copying. These findings thus offer the possibility of a role for an ancient RNA world on ice distinct from that considered in extant elaborations of the RNA world hypothesis. This work is, to the best of our knowledge, the first molecular dynamics study of RNA on ice.