In order to make him easier to manage, the Winter Soldier's handlers pick up crate training. At first, he's taught that his cryo chamber is his 'den' - it's a safe, enclosed space where he has his meals, and no one will beat him or yell at him inside. The training proves so successful that they introduce an actual cage for use in the field. (He'll hop into any car if it means he can crawl into his cage and curl up undisturbed for a couple hours.)

Bonus if this causes a problem post CATWS, where Steve/Sam/Natasha have to deal with a Bucky who is terrified of sleeping in 'people beds' and would rather shop at Petco.