Yes. You can wash your face even right after the cataract surgery. But, you shall keep in mind that do not let the water run directly into the eyes. So, you shall be carefully when you wash your face. Besides, after the surgery, you'd better not do computer work or watch TV within 2 weeks after the surgery. In addition, you shall also avoid swim.
Usually you could wash your face after two weeks from the date of doing cataract surgery, because there is the bacterium in the water which may come into your eyes when you wash your face. Then your eyes may get infection. Thus, you'd better use the warm cloth to wipe your face.
Of course, many people know this kind of surgery. As we know that through the surgery, it can improve your vision permanently. But on the other hand, there are also many things you should pay attention to it. For example, you can wash your face, unless you can make sure your eyes can not be moistened by the water. As we know that after the surgery, your eyes will be very sensitive and fragile. So if you let the water in your eyes, your eyes will be infected easily by the viruses. So just be careful about it. Also, you should pay attention to other things. For example, you should avoid eye injuries by wearing a protective shield at night and with naps until you are advised by your doctor. Also, you should remember not sleep on the side of the operated eye for the first night.