As of tomorrow it will have snowed for five days straight.

Literal

Tomorrow [with-で] 5-day snow [subject-が] continue-falling [nominalizer-こと] [dative-に] become.

Without でしょう, this reads as a direct assertion rather than a projection. ~ことになる marks a future result that 'comes about' — different from ~ことになっている (already arranged) in that this emphasizes 'it will turn out that.'