We don't know what he was or wasn't doing prior to visiting NYC at Christmas.
I don't know. If the BW scene is meant to be concurrent with Hawkeye, then I guess I'll just have to accept that the seasonal difference is just a blooper. After all, we've been told that the Hawkeye showrunners begged Marvel to be allowed to include Yelena in their show, so it seems like when they made the BW scene, they may have originally had a different idea of how Yelena's confrontation with Clint would go down.
Since Christmas is such an integral part of Hawkeye, we'll just have to ignore the fact that it was the "wrong" season during the BW scene.
It wouldn't be the first time such a goof made its way into the MCU timeline after all.