Put them in a warm (above 55 degree) and fairly humid place and let them dry out for 3 or 4 hours. You then can put them on a table or even on a concrete slab on top of several layers of newspaper or in cardboard boxes or rubber totes lined with newspaper. Spread them out enough that they are not touching one another and cure them for a couple of week before you move them to their long-term storage location. You should eat any damaged ones first because they'll spoil quickly.

Don't cure them at temps below 50 degrees though or they can sustain chill injury and that tends to make them spoil more quickly. I doubt that they sustained much, if any, harm from one freezing night because the ground itself likely did not freeze.

In the future, though, try to dig up your sweet potatoes and cure them before temperatures dip below 50 degrees as exposure to temps below 50 can cause chill injury which means they will be more prone to spoil. Since you left your sweet potatoes in the ground at a time when temperatures already were going lower than 50 degrees, they may have suffered chill injury and that means that they are more prone to spoil if held in long-term storage, so use them sooner (in a few weeks) as opposed to later (a few months). If you're going to use them next week, they ought to be fine. If you have more than you will use next week, cure the unused ones for a total of 2 weeks before you move them to a cool, dry place for long-term storage. (An unheated pantry or closet is a good spot to store sweet potatoes or even a box slid under a bed.) Properly cured sweet potatoes should last at least 2-3 months.

Dawn