"In order to get along with a Basenji, you have to be at least half as smart as the dog!"
Have you reported the posts and poster as spam? I don't know how much attention the moderator is giving this forum, but there certainly has been an increase in spam posts of late. The only other strategy I can suggest if it continues is to follow up the spam with relentless criticism of the product being advertised, and perhaps they will decide that bad publicity isn't what they were going for.....
Check for a UTI. Otherwise, she may have reached an age where she doesn't feel she wants to be uncomfortable, and she knows it is cold outside. For the next while I think I would take her out in the mornings rather than allow her to take the initiative via the doggie door.
Different situation, but perhaps a relatable example, my Border Collie was absolutely obedient his whole life, until the age of 14, when he decided that remaining in the field with me on a down stay when the day was hot wasn't to his liking, and he opted to return to the shade by the house. I think that as they age dogs sometimes decide that their comfort is more important than obedience. Or it could just be the onset of senility.