If you do not want to draw a fence separately and it is sufficient for you not to record any other properties of the fence (material, height, colour, etc.) then it is also possible to attribute an area as fenced, see here:
As usual in OSM, opinions differ widely as to whether this is a good way of mapping. However, you are always free to decide for yourself!
You can find discussions about this e.g.
here, here, here and some more here