Reinforcements and Frozen Moat

By mischraum.de, in 2. AGoT Rules Discussion

Okay reinforcements do not have printed strength and thus can be killed with Venomous Blade. But how about a text box?

Do they have a "virtual text" box that can be blanked with Frozen Moat and so they lose stealth, renown and deadly or do they have no text box and thus are the only characters that are immune to Frozen Moat?

Their abilities as a character card (strength, keywords, what have you) are a lasting effect originating from their printed Any Phase ability, lasting from the successful resolving of that ability until they leave play. Blanking their text box cannot affect that lasting effect, only their original Any Phase card ability as an event card, which at that point is not relevant any longer.