How far back, depends on how cold the winter was. And, an early warm spell followed by a cold snap in the spring will knock them back too. Some years, my crapemyrtles die-back almost to the ground. In other years, they might die-back only a foot. Last year, mine struggled. This year, they are doing great. A newly planted crapemyrtle that doesn’t have established roots will have a tougher go of it following a severe winter. You can wait and see what happens. Or, contact your garden center or landscaper and see what their policy is on replacing plants.
Thanks for writing!