You say it's broken-down, but that's not an ordinary sign. I don't think that's reparable, but if it's just cosmetic (not structural) I wouldn't worry.
Just a thought: perhaps that skate feels colder because your foot presses more on that spot? That could have caused the problem, so it might not have been a defect. IIRC, you bought these used and they were a little snug, right? (I might be thinking of someone else.) Stretching dry leather can cause it to crack this way. That doesn't mean the skate has broken down, although it is common for one boot to wear out before the other.
I would say to go to the skate shop and have them determine how broken-down the skate really is right now. If they're really shot, replace the skates. If not, and you can't feel the tear on the inside of the skate with your fingers, just tape it up well to get through the test.