Here's an interesting postcard from 1959. Either the woman mailing the card was confused, or
Truth or Consequences was holding some special contest in which viewers were asked to send postcards to T or C, New Mexico (in advance of the annual fiesta, perhaps?).
EDIT: Upon further investigation I see that there are a whole slew of these cards on eBay, so I guess it must have been a contest the show was holding in its eponymous town.