Answer: You were mistaken to abandon the prayers during the period you mentioned, for it is impermissible for a Muslim to leave the prayer altogether. Rather, he must pray in whatever manner his circumstances allow.
If you were able to perform the ritual ablution (wudu) with water, that was obligatory for you. If you were unable to use water—either because it was not available, or because, as you said, the cold was unbearably severe and you had nothing with which to heat it—then you were required to perform dry ablution (tayammum) with earth and pray. Should no earth be available, you must still pray according to your situation, even without water and even without earth.
Know that the term “earth” (saʿīd) is not limited to loose soil. If you had a wall on which there was clean dust, or a mat bearing clean dust, or even tiles with clean dust upon them, you could have struck them, performed dry ablution, and that would have sufficed. In short, what is required is the presence of pure dust—whether on soil, stone, a wall, a mat, or anything similar. Allah knows best.
Now that you have made up the prayers you missed, we ask Allah—may He be Exalted—to pardon you and to accept them from you.
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Cases in which a person is exempt
from the prayer entirely
Question: In what situations is a person completely excused from performing the prayer?
Answer: No one is exempt from performing the prayer so long as his mind is sound, for he must pray according to his condition. The sick person prays in the manner he is able: standing; and if he cannot, then seated, or on his side—and no one is exempt