These free verse lines do not adhere to any specific number of feet, nor to any regular distribution of stressed and unstressed syllables. So the poem is not in any regular meter.
The opening line suggests a catalectic dactylic trimeter:
| / x x / x x / x
| Softly I | walk through the | forest |
But the subsequent lines quickly dispel any notion that this poem is metrically regular. Neither the number of stresses nor their pattern is uniform from one line to the next.
| x / / x x | / x |
| The owl | sleeps in the | thicket |
| x / x / x x / x / x |
| I hear | the voice | of the lake | before me |
The first three lines themselves have dactylic (Softly I), iambic (I hear), anapestic (of the lake), and trochaic (thicket) feet, with an amphibrach (before me) thrown in for good measure. And while the first two lines have three stresses each, the third line has four. Such variable feet and irregular line lengths are a feature of the entire poem.
As a result of this unpredictability, some if not most of the lines can be scanned in multiple ways. For example, there is no obvious justification for preferring either of these ways of scanning line 7 to the other:
| / / x x / x x / x / x |
| All man- | ner of a- | nimals stand | beside me |
or
| / / x x / x x / x / x |
| All man- | ner of | animals | stand be- | side me |
The stresses are distributed too unevenly for any pattern to be discerned.
This is unsurprising in a late 20th century work. Like most writers after the First World War, the poet has chosen open form rather than closed form. Instead of metrical patterning, this lyric relies on repetition and cadence for its poetic effects. Subjecting it to prosodic analysis is beside the point.