Not only Haize but also Shirley and Joshua noticed that Jeremy's appearance remained the same when Frost Glacier took over it but the color of Jeremy's eyes became icy blue, which was similar to Jeremy's icy blue hair.
Jeremy's previous jade green colored iris became icy blue due to the influence of Frost Glacier's possession. But other than that change, there were no other changes in Jeremy's appearance other than Jeremy's change of demeanor.
Even if they didn't know that Jeremy was possessed by his ancient sword, they could still assume that Jeremy had multiple personality disorders and one of his personalities took over his body. That was Jeremy's current situation from their perspective.
After Frost Glacier had taken over Jeremy's body, he started to get familiar with his control over Jeremy's body. His purpose in doing that was to also stall time so that Haize's demonification duration would be depleted.
But how could Haize not know Frost Glacier's intentions?