Dairy Queen Postpones Free Cone Day In AmarilloDannyPublished: March 16, 2020Dairy QueenShare on FacebookShare on Twitter Dairy QueenIt’s a treat we all look forward to. Dairy Queen Free Cone Day. For the first time, DQ has announced that they are postponing Free Cone Day that was scheduled for Thursday, March 19th in light of the growing concern over COVID-19.