With the known chaotic nature of storm systems it wouldn't surprise me if the "butterfly effect" of the rounding errors when converting from C to F would be enough to displace a storm by hundreds of miles!

Absolutely not the case. First, all non-trivial computational fluid dynamics codes (e.g. those used for weather prediction) use non-dimensionalized values in the governing equations. You're not solving with C vs F (you'd never use either anyway, but absolute kelvin vs rankine), or meters vs feet, but non-dimensional numbers which are only converted back to dimensional ones after all the heavy computation is done.

Secondly, even if one were to use dimensional values in solving the equations, the round off errors for converting between C and F are many, many orders of magnitude smaller than the errors you get in the discretization of the original continuous system of equations.

Lots of comments here regarding metric vs. imperial units; I assure you that accuracy discrepancies between the European and American predictions have absolutely nothing whatsoever to do with any choice of unit system.

Source: I'm a CFD researcher =)