Does the effect of Mask Mother count as an additional cost and is reduced by Ezreal?

No. Mask Mother's ability is a triggered ability with a cost within instructions ("you may pay [1] to give +2 [S]"), not an optional additional cost, so Ezreal, Prodigy's discount does not apply.

Ezreal only reduces costs that use both "as an additional cost" and "may" (Rule 356.2.b, FAQ #8415/#9237). Mask Mother's [1] payment happens during resolution of her trigger, in the form "[do X] to [do Y]" (Rule 204.3) — the same reason Ezreal can't discount abilities like Draven's attack/defend cost. Even though it says "may," it's not an "additional cost" to play anything, so the [1] stays full price.