The poem as a whole is concerned with the continual nature of life in the midst of hardship, whether that be physical or mental. The narrator comments on the cold, gray frost that covers the landscape; for a bird, this weather is not conducive to a pleasant life (aside from keeping predators mostly docile). However, the thrush sings in the middle of its hardship, showing that it believes (either rationally or instinctively) that things aren't so bad.
So little cause for carolings
Of such ecstatic sound
Was written on terrestrial things
Afar or nigh around,
That I could think there trembled through
His happy good-night air
Some blessed Hope, whereof he knew
And I was unaware.
(Hardy, "The Darkling Thrush," poets.org)
The overt religious imagery is explained elsewhere, so the question remains whether the thrush itself is spiritually motivated to sing. It cannot be religious, since that requires sentient thought; instead, it might be motivated by an instinctual spirituality that natural living things share. While humans can think about their reasoning, the thrush acts on its biological programming. If that programming were placed there by a spiritual force -- such as God -- then the thrush would instinctively know to sing in praise of that force, both for its own benefit and to spread that love to other creatures. The narrator muses that the thrush might be aware of something -- Hope -- that he cannot comprehend; perhaps the narrator is too wrapped up in rational thought to remember his hereditary instincts, and only now realizes that there will always be life, beautiful and unique, in the midst of even harsh conditions.