Note: I forgot to mention the hose has diameter of about 5/8"

Sounds like the rear axle vent?  Just tie it up out of the way for now.

So wait - both ends are loose?  Like BIR said, it sounds like it's the rear
axle breather hose.  Look on top of the rear axle, driver's side.  You'll
see a brake distribution block (two hard lines running out to each wheel,
one flex line running up the the left-side frame rail).  There should be a
hose barb sticking up from this block, and that's where the hose connects
to.  The other end, with the white plastic piece in it (that's the
breather - it's got tiny holes to allow air to pass, but keeps any water
spray out), should have a metal clip on it, and it clips up to the spare
tire carrier frame.  If the clip is gone, just use a zip tie to secure it,
and use a small hose clamp to clamp the hose to the hose barb on the axle
tube.  Be sure to leave a little slack in the hose, so that the suspension
can droop without straining the hose.