Cold cream is an alternative to soaps and other facial cleansers and is often used to remove heavy makeup and cleanse the face. This is usually a fairly heavy cream, but you rinse it away after using it.
Cold cream can be used if you have oily skin, but you may not want the extra moisturizing cold cream provides as a cleanser. There are a variety of cold creams on the market, ranging from very rich to very light moisture, so if you do choose to substitute a cold cream for your facial cleanser and makeup remover, do so with one that will only lightly moisturize your skin. This will help retain moisture, but not over-moisturize your skin to the point of retaining more oil than what is washed away.
Cold creams are good for people with combination skin, as it works well to get rid of oil and dirt in the t-zone, but also hydrates the chin and cheeks that may otherwise get dry with other cleansers.