Can Frigid Jewel trigger more than once per turn, for example drawing 6 cards?

No — Frigid Jewel triggers at most once per turn.

Its condition is "when you draw your second card each turn" — there's only one second card per turn. If you draw 6 cards, the ability fires on the 2nd draw and that's it; the 3rd–6th draws don't satisfy the condition. Even if you draw multiple cards at once (e.g., "draw 3"), you pick which one counts as the second and the ability triggers only once (Rule 383.1.b). It resets each turn, so a new turn's second draw can trigger it again.

Per FAQ 10414, the only thing that matters is which draw is the second one that turn — everything after is irrelevant.