They've always been cool!
HOM was the only title that started out as Precode and made it to the Bronze Age. It drifted into sci-fi and some quirky superhero tales (J'onn J'onnz, Dial H for Hero) before it settled on the horror/mystery format in issue 174. House of Secrets which came later, made a similar change at issue 81. These are the start of the early Adams and Wrightson issues.
The ban on horror was not so much lifted (as the code was still in effect) but it eased up quite a bit and let vampires, werewolves, demons and such be reintroduced back into storytelling.
This. In a nutshell; the DC Mystery line was revamped in 1968 under the editorship of Joe Orlando. House of Mystery became new at #174, House of Secrets at #81 (1969) - as for Unexpected, see my question above.
Imagine being a young, unsuspecting HoM/Dial H for Hero fan in 1968, and then being greeted by #174 on the stands!