Any process that results in a change in state or activity of a cell (in terms of movement, secretion, enzyme production, gene expression, etc.) as a result of a cortisone stimulus. Cortisone is a natural glucocorticoid steroid hormone that is metabolically convertible to cortisol. Cortisone is synthesized from cholesterol in the cortex of the adrenal gland under the stimulation of adrenocorticotropin hormone (ACTH). The main physiological effect of cortisone is on carbohydrate metabolism; it can stimulate increased glucose release from the liver, increased liver glycogen synthesis, and decreased utilization of glucose by the tissues.