You missed that Double Horse Kick is a "SPECIAL MOVE!1!11!11!" and ignores all abilities on the field, so Normalize should not affect this calc. I don't see a Horse-type on the horse, but I did a separate calc with STAB anyway. Unfortunately the Silk Scarf only boosts Normal-type attacks.
252+ SpA Mudsdale Double Iron Bash (2 hits) vs. 252 HP / 4 SpD Toxapex: 78-92 (25.6 - 30.2%) -- approx. 4HKO
252+ SpA Mudsdale (STAB) Double Iron Bash (2 hits) vs. 252 HP / 4 SpD Toxapex: 116-138 (38.1 - 45.3%) -- approx. 3HKO
252+ SpA Choice Specs Mudsdale (STAB) Double Iron Bash (2 hits) vs. 252 HP / 4 SpD Toxapex: 170-204 (55.9 - 67.1%) -- approx. 2HKO
EDIT to below:
It says special in your description, not physical or status. Since the horse-type didn't exist in generations before the physical/special split happened, there are really no other inferences we can go off of.