I planted my seed potatoes in March in containers and put them outside. We had cold days and even snow once.
Will my seed potatoes still be able to produce potatoes?
Unless your containers are very small and the cold was very deep, there is a good chance that the potatoes will be fine. It takes a lot of cold to freeze a container entirely, and even then the potatoes are exothermic - the heat on the inside of the mass of the tuber will protect the surface where the eyes are from freezing. I'd say at least 98% chance that a tuber that was healthy when planted will survive just fine.
In their natural life cycle, the potatoes would have been in the ground all winter, and would start growing in spring when the soil temperature is right for them.
Unless they have been frozen and killed (which isn't very likely), they will grow just fine when the conditions are right.