That night's watch character without challenge icons...

They can be played in any challenge or what?

Thank you

You'll want the Night's Watch agendas to give your characters icons:

The Stewards

The Builders

The Rangers

Also, with The Wall, NW characters can defend even if they lack the appropriate icons.

There are also attachments (and other effects) that give icons to characters. A character without icons cannot be declared attacker or defender in any challenge (but some effects, like The Wall, let you put them into play as defenders nonetheless). They just count their strength for dominance and can be used to pay costs.