Are the number and colours of cards in player's hands private information?
From the rules link here it says on page 2.


  All information on a
  player’s vineyard mat as well
  as available workers, amount
  of lira, and number of cards
  is public information and
  cannot be concealed.


This specifically says 'All information'  That would certainly include the colour on the back of the card.  If a player has to clearly display how many cards they have when asked then the colours will be visible.

The game didn't come with screens and cards are also taken from stacks publicly so I see no reason why it would be then secret.  It strikes me that your opponent refusing to tell you is incredibly unsporting and just that player trying to gain what every spurious advantage they can!