This looks to be James White's "The Dream Millennium" as serialized in Galaxy magazine from October to December of 1973 (below excerpt from the December 1973 edition of Galazy magazine):
JOHN DEVLIN is awakened from
cold sleep by ship’s computerized
system and told he’s seventy-five
years into mission: man’s first attempt to colonize a star system other
than his own. He is computer-instructed to check ship’s systems,
then his own voluntary /involuntary
bodily functions, circulation, sensorium, speech organ and memory. His
period of awakening is for one hour.
During this time he is to speak,
exercise and try to remember his
cold-sleep dream. In his dream he
was a primitive, ocean-dwelling life
form, inordinately hungry -and was
himself eaten by a carnivorous cephalopod while eating a trilobite.
His second awakening comes 282
years into mission. His instructions
are as before, but in addition he’s
told to go to the ship's control center
to evaluate target system three. The
ship’s computer had bypassed the
first two target star systems as unsuitable for human colonization.
Number 3 is a perfect, Earth-type
planet, unpolluted and verdant-but
is entering Roche’s limit and will
soon break up to become a ring
system around its primary . DEVLIN
rules no landing, obediently remembers last cold-sleep dream: in it he
was an enormous brontosaurus and
was killed by a small, carnivorous
Found with search terms of "cold sleep" trilobite on Google Books, and then searches on the text excerpts I found from there.