The only evidence I found of Tess sleeping in the woods by herself can be found in the text below. I see no mention of a beautiful forest animal, only the pheasants cited below.

Day at length broke in the sky. When it had been day aloft for some little while it became day in the wood.

Directly the assuring and prosaic light of the world's active hours had grown strong, she crept from under her hillock of leaves, and looked around boldly. Then she perceived what had been going on to disturb her. The plantation wherein she had taken shelter ran down at this spot into a peak, which ended it hitherward, outside the hedge being arable ground. Under the trees several pheasants lay about, their rich plumage dabbled with blood; some were dead, some feebly twitching a wing, some staring up at the sky, some pulsating quickly, some contorted, some stretched out—all of them writhing in agony, except the fortunate ones whose tortures had ended during the night by the inability of nature to bear more.

Tess guessed at once the meaning of this. The birds had been driven down into this corner the day before by some shooting-party; and while those that had dropped dead under the shot, or had died before nightfall, had been searched for and carried off, many badly wounded birds had escaped and hidden themselves away, or risen among the thick boughs, where they had maintained their position till they grew weaker with loss of blood in the night-time, when they had fallen one by one as she had heard them.