A three-component system consisting of butylammonium vermiculite, butylammonium chloride, and water was studied by X-ray and neutron diffraction experiments in freezing cycles between -5 and +5 degrees C. In liquid water, all the samples studied were in a colloidally swollen gel phase, with interlayer separations between the clay platelets of the order of hundreds of angstroms. Upon freezing gf the water, the colloidal state collapsed into a tactoid phase with an interlayer separation of d = 19.4 Angstrom. This phenomenon was observed throughout a wide range of clay concentrations r and salt concentrations c. The phase transition was observed to be reversible, the gel phase always being recovered upon warming through the freezing point of water. Such a reversible phase transition between swollen and collapsed clay mineral phases may be important in the weathering of rocks in freezing cycles.