A Red Velvet is suppose to be crumbly . However, chilling / freezing it causes solidification and clumping of the insides making it hard.
Not good.
However, in reality, the cheese cream will need freezing or else it would spoil really quickly or won't even set in the first place if the cake's just been creamed, so , the compromise is to have a chiller with a higher setting and taking the cake out about 20 min or more before the next serving.
Q