out of the woods

out of the wood(s)

No longer in danger or dealing with a particular difficulty, though not entirely resolved. Usually used in the negative. Her surgery went as well as we could have hoped, but she's not out of the woods yet. If our sales stay strong, we should be out of the woods by the next quarter.
See also: of, out
Farlex Dictionary of Idioms.

out of the woods

Fig. past a critical phase; out of the unknown. When thepatient got out of the woods, everyone relaxed. I can give you a better prediction for your future health when you are out of the woods.
See also: of, out, wood
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.

out of the woods

Out of difficulties, danger or trouble, as in We're through the worst of the recession-we're out of the woods now, or That pneumonia was serious, but Charles is finally out of the woods. This expression, alluding to having been lost in a forest, dates from Roman times; it was first recorded in English in 1792. The British usage is out of the wood.
See also: of, out, wood
The American Heritage® Dictionary of Idioms by Christine Ammer.

out of the woods

mod. freed from a previous state of uncertainty or danger; no longer critical. As soon as her temperature is down, she’ll be out of the woods.
See also: of, out, wood
McGraw-Hill's Dictionary of American Slang and Colloquial Expressions

out of the woods

Informal
Free of a difficult or hazardous situation; in a position of safety or security.
See also: of, out, wood
American Heritage® Dictionary of the English Language, Fifth Edition.

out of the woods

Out of trouble or danger. The image of emerging from a dangerous forest goes back at least to Roman times. The playwright Plautus used it (in Menaechmi, ca. 200 b.c.), as did other Roman writers. In Great Britain it is usually put as out of the wood.
See also: of, out, wood
The Dictionary of Clichés by Christine Ammer
See also:
  • save someone's skin
  • heaping Pelion upon Ossa
  • save (one's) own skin
  • save skin
  • screw up (one's) courage to the sticking place
  • on red alert
  • come up against
  • come up against (something)
  • there's trouble brewing
  • trouble brewing