That is probably a ficus benjamina, commonly called a weeping fig.  If you allowed the branches to grow they would assume a weeping  shape.  You do not need to cut off the leaves but just bring it in and give it good light and care for it as a house plant over the winter.  Some of the leaves will fall off but new smaller leaves will develop.  Do not overwater. Weeping Fig (Ficus): Plant Care & Growing Guide (thespruce.com)