Yes, it is possible. Tears can freeze when it has to be 40 degrees below zero only. In general, the skin would keep tears warm on the face. So the temperature outdoors needs to be cold enough that your cheeks start to freeze to lead to tears to freeze. And you have to be outside for a very long period to see that, which means your tears would have to stay parked on your face for an equally long period.
In the usual situation, the tears will not freeze. However, only below zero with the very cold temperature can the tears be freeze. However, this is difficult to get the tears to be freeze. Besides the cold temperature, only getting the set point can the tears be freeze. If you get the freeze tears, you will be so uncomfortable.
Well, I wonder if you live in a warm place, because it is a natural thing to have frozen tears in winter. As a matter of fact, in some extremely cold areas, when we shed tears, the tears could go frozen because of the extremely chili whether. So, it is quite normal. What's more, when we pee, a few seconds later, the mess could also go frozen. Just wear more and stay in the room.