Does Frigid Jewel in play count Stacked Deck as draw 1 card?

No. Using Stacked Deck while Frigid Jewel is in play will not trigger its ability.

Frigid Jewel looks for when you draw your second card each turn. Stacked Deck instructs you to "put 1 into your hand" — that's a distinct game action from drawing (Rule 413.1). Since it isn't a draw, it doesn't advance the count toward the second draw, so Frigid Jewel's trigger condition is never met.