Historical Context in Ode on a Grecian Urn
Most likely the priest of Hera, queen of the gods, or Hymen, god of marriages. In ancient Greece, both these gods traditionally presided over weddings, requiring that a heifer (or cow) be sacrificed in order to bless the marriage.
In ancient Greece, the pastoral referred to the ideal state of nature. In poetry, the pastoral is a type of poetry that glorifies that ideal nature. It's described here as being "cold" because, though not technically alive (or warm), it still lives forever.