Can a mixture of water miscible solvent and water be separated by fractional freezing on a dry ice bath?
The short answer is 


  Yes


This is exactly how acetic acid is purified: Acetic acid freezing distilation

In this case, acetic acid (freezing point $16\ ^\circ \text{C}$) freezes first, leaving a water-enriched fluid behind. Conceivably you could remove water from methanol or acetone in the same way (except that water would freeze first). In practice, fractional distillation can be done more economically on a large scale. Fractional distillation requires 1 step (with lots of theoretical plates), while you need to repeat fractional freezing multiple times to get to high purity. Acetic acid is purified by fractional freezing perhaps because it may azeotrope with water.