Supernovae generate all the heavier elements, but not molecules like water (if that is the "ice" you mean - "ice" is sometimes used to refer to other solidified liquids). Such molecules would form as the elements cool down. The hydrogen existed from the beginning of the Universe. Oxygen is formed in most stars, not only in nova and supernovae.
Some reading:-
http://ftp.astronomy.ohio-state.edu/...supernova.html
and the actual lecture to listen to:-
http://ftp.astronomy.ohio-state.edu/...dio/Lect18.mp3 (16MByte mp3 file)