Found a few other references to sleeping/waking plant life (mostly trees):
in the Old Forest:
"I [Merry] have been in several times: usually in daylight, of course, when the
trees are sleepy and fairly quiet."
Old Man Willow:
"What be you a-thinking of? You should not be waking. Eat earth! Dig deep!
Drink water! Go to sleep!"
in Fangorn:
"Some of us are still true Ents, and lively enough in our fashion, but many are
growing sleepy, going tree-ish, as you might say. Most of the trees are
just trees, of course; but many are half awake. Some are quite wide awake, and
a few are, well, ah, well getting Entish."
Could it be that the trees of Fangorn were awake, and the forest was rising,
marching over the hills to war?
leaving Ithilien:
"The land dreams in a false peace, and for a while all evil is withdrawn."
About them lay long launds of green grass dappled with celandine and anemones,
white and blue, now folded for sleep ...
the White Tree sapling:
For it is said that, though the fruit of the Tree comes seldom to ripeness, yet
the life within may then lie sleeping through many long years, and none can
foretell the time in which it will awake.
***********************************
Another unlikely object that "wakens" is Isildur's Bane.
As for the right season for turnips & carrots & taters, they're all root crops
and need some time to grow after the ground has
thawed.

"Watch every shadow!" he said in a low voice.
"Black horsemen have passed through Bree."