Leaves wilt, and then turn black, then crispy over the course of 3 days. Extremities affected first/most severely.
Early varieties of potato are affected most by frost. Unless it has been particularly harsh plants should recover. Check for new growth to evidence life in the plants.
Check the weather forcast and cover with fleece if frosts are expected. Check growing hardiness of plants and growing instructions to see when they can be left outside without protection.