My understanding is that in a typical groundwater pond with little change over of the water from intake of new water (runoff/creek water) or little outflow of water produces a situation where aeration is not needed year around. 12' is a typical depth where there should be less chance of winter kill due to the warmer water layer right at the bottom.

Winter aeration would be an option if you choose to have another shallow water 'warm water' refuge area for fish to try to avoid winter kill. There are other ways to avoid winter kill for those of us who try to keep the ice strong for ice skating (plants to make O2 under the ice, keeping the ice clear of snow for sun penetration). But with a one acre pond you have plenty room for skating and to still leave an area open to meet both goals.

When the water is cold the oxygen carrying capacity is the highest. There is no thermocline yet and the entire pond water is probably around 37 at the bottom and around 40 at the best at the top on a sunny day. Aeration's job is to move bottom water up towards the top and your water is already pretty well mixed throughout.

Well into spring if you have wind action you may still have plenty of aeration action and moving around/mixing of the water. When water temp differences get bigger from top to bottom then it makes sense to turn on the aeration.

If you decide to run your aerator when the water is cold (early spring) some run it purposely in the warmest hours of the day to try to help 'wake up' the pond faster by exposing more of the water from the bottom to the sun at the top. Then as the temp differential builds and you start getting a 15 or 20 degree swing between bottom temps and top temps then many of us turn our aerators to 8-10 or 12 hours only at night (an hour or two before dusk to an hour or two after dawn). This tries to then keep the water cool in light of the oncoming summer dog days. The cooler water then keeps fish less stressed, keeps oxygen content higher, slows down algae growth, etc.

Just some thoughts.