Sorry to be guessing at this one... but when you say your outside pipe ... do you mean the overflow..?
If your overflow is blocked it may well be ice blocking it ... but the only reason to have water flowing down your overflow is because your filler valve in the cistern needs adjustment or replacing ... it certainly does if the water is reaching the overflow.
Have you got a service valve on the pipe supplying water to the cistern... if you have turn it off, and this will stop the need to keep removing water from the cistern. Then the filler valve can be sorted.
This problem sounds very similar to a thread earlier in the week ...
http://www.theanswerb...n/Question968922.html