Yes and no. It depends on which glaciers you are considering. Parts of the Antarctic Continent have had continuous glacier cover for perhaps as long as 20 million years. Other areas, such as valley glaciers of the Antarctic Peninsula and glaciers of the Transantarctic Mountains may date from the early Pleistocene. For Greenland, ice cores and related data suggest that all of southern Greenland and most of northern Greenland were ice-free during the last interglacial period, approximately 125,000 years ago. Then, climate was as much as 3-5o Fahrenheit warmer than the interglacial period we currently live in.
Although the higher mountains of Alaska have hosted glaciers for as much as the past 4 million years, temperate glaciers in Alaska are generally much, much younger. Many formed as recently as the start of the Little Ice Age, approximately 700 years ago. Others may date from other post-Pleistocene colder climate events. Some, such as the glaciers in the summit craters of Mount Redoubt and Katmai Volcanoes, have reformed following eruptions during the 20th century.