I've been estimating continuous positive outcome Poisson regression with the Huber/White/Sandwich linearized estimator of variance fairly frequently. However, that's not a particularly good reason to do anything, so here are some actual references.

From the theory side, $y$ does need to be an integer for for the estimator based on the Poisson likelihood function to be consistent. The data does not even need to be Poisson. This is shown in Gourieroux, Monfort and Trognon (1984). There's also some encouraging simulation evidence from [Santos Silva and Tenreyro (2006),][1] where the Poisson comes in best-in-show. You can also easily do your own simulation to convince yourself that this works in your snowflake case.

Finally, you can also use a GLM with a log link function. Often, this yields similar results and placates the count-data-only knee jerk reactions.


**References Without Ungated Links:**

Gourieroux, C., A. Monfort and A. Trognon (1984). “Pseudo Maximum Likelihood Methods: Applications to Poisson Models,” *Econometrica*, 52, 701-720. 


  [1]: http://personal.lse.ac.uk/tenreyro/jensen08k.pdf