is there a dress code at the river cafe?

Yes. Women: dress, men must wear a jacket

Is it cold in the terrace room

From website: Jackets are required for gentlemen for dinner and anytime after 4 PM. Ties are preferred. Weekend Lunch and Brunch can be slightly casual, but too casual is never allowed. Appropriate footwear is required at all times.

There is no dress code for lunch. For dinner, men just wear jacket.

Yes. Women must wear a dress. Men must wear a jacket.

Yes. Men must wear a jacket. Just call them, they'll tell you.

Yes, minimum of dress coat (not winter jacket) for men.