Previous Fourier-transform infrared spectroscopic studies of adsorbates on the surface of ice nanocrystals have considered two categories of molecular adsorbates : (a) weak adsorbates that desorb rapidly into a vacuum at T < 100 K and that influence the vibrational modes of only the surface molecules of ice and (b) adsorbates that form significant H bonds to the unsaturated surface groups resist desorption at temperatures below similar to 120 K and, without penetrating the ice, alter the subsurface ice spectrum. Here, we consider a third category of adsorbates which is characterized by molecules that form strong H bonds with the ice surface, penetrate the ice, and form hydrates. It is shown that above some minimum temperature of adsorption strong acids and Lewis base molecules, including ethers and amines, penetrate the ice and ultimately form known crystalline hydrates of the adsorbate. Results are reported for HCl, ethylene oxide, and ammonia as representative of these three subclasses of penetrating/reacting adsorbates. Ethylene oxide is shown to convert nanocrystals of ice to nanocrystals of the type I clathrate hydrate at 130 K. Similarly, nanocrystals of ice, exposed to NH3 at 120 K, convert slowly to nanocrystals of the monohydrate of ammonia by a molecular reaction mechanism. By contrast, HCl, following adsorption in the 60-125 K range, converts ice nanocrystals to the amorphous ionic monohydrate which crystallizes upon warming above 135 K. However, below 50 K, adsorbed HCl exists primarily as the molecular adsorbate with a behavior similar to that observed for adsorption on amorphous ice. Disorder associated with the surface reconstruction of bare ice and the presence of strained H bonds between water molecules of the relaxed surface are likely critical factors in the interaction/reaction with adsorbates, such as atmospherically important HCl. However, the ability of strong proton donor/acceptor molecules to break and replace stable H bonds to water molecules is considered a prerequisite for the observed complete conversion of ice nanocrystals to hydrates at cryogenic temperatures.