Iron deficiency is relatively unlikely in heavy drinkers as alcohol itself enhances iron absorption and wine is a relatively good source of the mineral though it may not always be well absorbed.
Heavy drinkers are unlikely to need iron supplements and multivitamins with iron should not be taken by anyone with abnormal liver function tests as they may have an excess of iron. This can be due to the genetic condition haemochromatosis which results in increased iron absorption leading to iron accumulation in the liver and elsewhere causing fatigue, liver disease, arthritis, diabetes and hormonal changes in men and women.
Supplements of iron should not be taken by heavy drinkers without tests to determine what their needs are. Multivitamins with iron should not be taken by anyone with persistently abnormal liver tests unless they have been demonstrated to be deficient