After every one of the WS's missions, there is one Hydra agent tasked with cleaning the asset in preparation for cryo.

This agent (could be a character or just an anonymous hydra goon) strips the Winter Soldier down and washes him, taking as many liberties as he wants during the process.

The Winter Soldier obeys every order and lets himself be handled, but it's up to filler if he dreads the rape, looks forward to it or is indifferent.