In most cases, itchiness/dry skin around the vaginal opening in post-menopausal women is due to a decrease in estrogen. Estrogen is the hormone responsible for the maintenance of vaginal tissue and lubrication. During menopause or after a total hysterectomy with bilateral salpingo-oophorectomy (surgical removal of the uterus, fallopian tubes, and ovaries), there is a marked decrease in estrogen which results in atrophy of the vaginal tissue and decrease in lubrication. The result is thinning of tissue, itchiness/dryness, and occasionally inflammation.
There are lubricant creams that can be applied as well as hormone replacement creams. If the itchiness and irritation persists despite treatment, you should be evaluated by a medical professional as it could be a sign of a serious medical condition.