Ammonia, a polar molecule (NH3), has a melting point of -77`C.

If liquid ammonia at -50`C was kept at this temperature, is it possible to dissolve ice (H2O) in it?

(or dissolve solid H2O in any polar liquid, for that matter...)

What we are concerned about is regarding the equilibrium temperature (in relevance to an closed system and q=ms(dT)) upon adding ice; we don't wish it to reach anywhere near the freezing point of ammonia (assuming ammonia constituted a much larger portion). I would imagine that in most cases ice would dissolve in ammonia and that the reaction in most cases would be slightly exothermic...hydrogen bonds can be formed in the solution and the entropy change would probably be positive.

Yes ammonia does dissolve ice, some poeple use it on special machines to keep ice at bay.