In spite of the benign microclimate of El Calafate, you have to think that the closer you get to the Glaciers, the colder it gets.
This is why you must have a warm jacket and appropriate footwear, the ideal are trekking style boots, leather soled shoes or nautical sneakers are not recommended. It is also important to have several pairs of socks.
In spite of these clothing recommendations the most adequate thing to do is to dress “onion style”: in layers, because all the interiors (hotels, restaurants and transportation means) are very well heated.