Hi Joe,
No direct experience with snow fluid and woodwinds, however, even though the fluid says that it's "no-residue" formula, I usually find there's a residue afterwards. Also, generally speaking my experience has been that musicians aren't hot on the idea of liquids falling onto their instruments... You may want to check with them before you incur their wrath.
Does your director know how loud these machines are? Can you go with a paper or plastic snow effect with a tumbler or snow bag?
Just some thoughts.
Chad