yeah it does! long story, i was with a mate on holiday, we were drunk and bored...and made a rather bizarre mixture of different things, one happened to be washing up liquid, it went in the freezer over night, et voila! - frozen washing up liquid!
Depending on the ingredients, it will probably start to freeze at around -10�C (14�F). So in a domestic freezer, which has an operating temp of around -18�C, sounds about right.