Cool air, clear skies and light or calm winds are necessary for frost to occur. Cool air permits temperatures to drop low enough to freeze moisture in the air which would otherwise form dew. When skies are clear, heat from the soil is able to rise, allowing the cool air to settle close to the ground and chilling the plants as they lose heat.
Calm winds allow the cool air to settle without mixing it with warm air.
The critical feature is the internal temperature within plant tissues. If temperatures within these tissues are cold enough to break cell walls or disrupt cell constituents beyond repair, damage, wilting, and dying will occur in those tissues affected. Some plants are more tolerant of frost than others. Woody plants are less affected than succulent plants. Fruits and flowers may be more sensitive than leaves.