Is it
An annual plant
I awake, refreshed anew.
The plant comes back to life, refreshed and looking new
Looking forward to a new and glorious day, I unfurl and quiver in the cold.
Looking forward to a new period (year) of living, it comes back to life when it's still cold outside
My morning shower wakes me and regales with many succulent droplets; I can feel them invigorate my veins.
The morning is the end of winter and start of spring, there's still a lot of rain but that helps the plant to grow and gain strength
I start my work.
It start's with photosynthesis when big enough
I remember to breathe in and out.
Breathing in carbon dioxide and breathing out oxygen.
As the day unfolds I thirst and deeply drink my fill.
The plant tries to fill up on water as much as possible, so it can survive the summer
The heat of midday is relentless, but I am virile; I weather the storm.
The midday represents the summer. A period with a lot of heat but also a storm from time to time. Only strong and virile plants survive this.
At day's end, I grow tired, but I cling to consciousness.
The end of the day is autumn. The plant starts to lose its strength but still lives. It's ready to end its life cycle for this year.
I find myself once again chilled and shivering.
Winter is coming, the cold is back
Eventually, I gravitate back to bed, digging deep into the cover.
The plant has no strength left and dies, disappearing back into the earth
I dream of my ancestors, remember my roots.
The plant may be "dead" but the roots are still there, ready for a new cycle. The ancestors are the past lifecycles.
And sleep.
The roots are asleep all winter
Tomorrow is another day.
The lifecycle starts anew with a new "day" which represents a new annual cycle.
The hint explained
The day talked about is the annual cycle from life to "death" covering all the seasons. The climb is the growth of the plant.