If the water froze in the washer bottle it could have caused the fuse to blow rather than overload the washer pump.
I saw from your other post that this may have been the case.
Depending on the quality of the washer additive you will probably need at least a 1:1 mix in the current weather to give protection down to about -10 Centigrade. Ready mixed screenwash may not be concentrated enough to stop the water freezing at this sort of temperature.