An extended period below 20 o F can degrade the final harvest quality. Even so, overwintering is still your best chance for getting large onions. Onions aren't just a leafy vegetable. And they need these nutrients throughout the growing period. The soil should be fertilized before planting and a side dressing should be applied at the beginning of bulb formation.
Onions are shallow-rooted.
To adequately supply the water requirements of onions, you should water more frequently with smaller amounts of water. After the plants are established, don't let more than an inch of soil dry out between waterings. Often, a layer of straw is applied as a moisture conserving mulch. Any drought stress will set back your onions possibly causing them to bolt. Top quality, large bulbs require consistent care but they are well within the reach of the home gardener.