Originally Posted by Blueskies21

The ODH has a wind chart showing degrees off runway heading and speed to find associated headwind/tailwind and crosswind.

The Category II briefing checklist from the ODH has the respective limits for headwind, tailwind, crosswind and is required to be used by the Captain for a Category II approach.

So in answer to your question, I'd say the Captain is checking. However, having been a First Officer, I always checked myself as well, there's a reason there's two pilots in the cockpit, none of us are infallible. As a Captain, I always suggest that my FO's check things themselves as well. So take that answer however you will.

As msprj2 noted, you CAN always input the wind in the ACARS (and in the case of a tailwind it's required), if you exceed a wind limit the ACARS landing data will generally come back blank but I'm not sure that would occur with the lower Category II wind limitations, I think it only happens for an aircraft limitation.