Does Vex increase cost when going a battlefield and the opponent wants to play a hidden card?

Yes, Vex, Cheerless increases the cost of your opponent's hidden cards if they are played while Vex is in combat at that battlefield.

According to the official RiftJudge FAQ #620 and FAQ #8518:

1. Hidden sets the base cost of the spell to 0.
2. Vex's passive ability acts as a cost increase for enemy spells, which is applied after the base cost is set to 0.
3. Therefore, the final cost to play the hidden card is the base cost (0) plus the additional cost imposed by Vex (1 Energy + 1 Power).

Important Nuances:

• Combat Requirement: This cost increase is only active while Vex is in combat at a battlefield. If Vex has moved to a battlefield but combat has not yet initiated (for example, while other "When I move" triggers are still resolving), the cost increase is not yet active.
• Sequence:
  1. The player chooses to play a card from Hidden.
  2. Hidden sets the base cost to 0.
  3. Vex's passive ability is applied as a cost increase, raising the total cost to 1 Energy + 1 Power.
  4. The player must pay 1 Energy + 1 Power to complete the process of playing the card.