Moles are not usually treated with freezing (cryotherapy). Some abnormalities of the skin (lesions) can be successfully treated with freezing, for example seborrheic keratoses. I suggest you get the opinion of a suitably qualified and experienced doctor.Best wishes.
Freezing moles will not remove the entire lesion as there is a deep component to a mole that is not reachable with standard cryosurgery procedures. Some lesions that are removed by freezing include seborrheic keratoses and soft fibromas as these are more superficial. Some patients confuse moles with keratoses. So it is really important to qualify exactly what type of lesion is being removed. If the lesion is truly a Nevus or mole, it is better removed with surgical excision so that there is pathology.