How does Helm of Suppression interact with hidden cards? Does it increase the cost of revealing them?

It depends on what was hidden. Helm of Suppression only raises the cost of spells, so:

• Hidden spell: Yes — playing it from Hidden still counts as playing a spell. Hidden sets its base cost to 0 (Rule 811.1.b → 356.1.b), but cost increases apply afterward (Rule 356.3), so it costs [1] more (or [1][A] more if Helm is Empowered). Same logic as the Fizz ruling (FAQ #11727).
• Hidden unit or gear: No — they aren't spells, so Helm does nothing to them.
• The hide action itself: No — hiding costs 1 Power (recycle a rune) and isn't playing a spell, so Helm never touches it.

Net effect: Helm makes revealing a hidden spell not-free, but leaves hidden units, gear, and the hiding cost alone.