Yes, freeze/thaw tannin precipitation using plain water is a pretty neat idea - I suspect it works almost like freeze-precipitation from naphtha does, except that the freeze-precipitated tannin redissolves much more slowly than DMT does (which, incidentally, is likely to be because of both the larger molecular size of the tannin acids, as well as their larger amount of hydroxy groups which produce strong intermolecular hydrogen bonds in the aggregated solid).
My experience with aqueous alcohol at around 35 - 40% ABV has been that, below around -24°C, the large proportion of water freezes into a single solid matrix of interwoven crystals which trap any remaining liquid alcohol in the interstices, and the viscosity of the alcohol along with capillary forces causes it to remain trapped to the extent that it effectively means the whole thing has solidified. The freezing point of pure ethanol is something like -114°C, which means that you'd need liquid nitrogen as a refrigerant - at least as the most readily accessible one - if you didn't have a specialised laboratory cryorefrigerator.
Fortunate, then, that freezing of pure (or azeotropic) ethanol is probably not necessary here. It would seem worthwhile to test out sticking the raw vodka tincture, tannins and all, straight into the freezer to see what drops out. In that instance we'd have to check whether any proportion of the alkaloids sticks to the precipitated tannin. If this proves to be an issue one option would be to acidify the tincture before freezing. This would become an alternative to the lime precipitation if it removes sufficient amounts of tannin and keeps the alkaloids in solution.
Once we've got a better grasp of all the data points here I think it would be prudent to tabulate all the options regarding ethanol-based extraction into a flow-chart for. This would help people to decide how to proceed with their extractions depending on the local availability of materials. It should also be tested with other plant materials to see if freezing or lime treatment serve to clean up other things besides tannins.
As a final footnote, I think freezing of vodka-strength tinctures is useful to remove excess water, which leads to an easier evaporation process afterwards - I also have a hunch that it will be a better product the higher the %-age ABV prior to evaporation, and this may well apply to citrate honey precipitation from the tinctures too (another thing to be tested!)