my contractor needs to move the floor vent to the new closet wall. His plan is to simply partially close off the floor vent, then build the closet wall over the remaining portion, allowing the air to just flow into the closet wall and out a vent which he will install about a foot off the ground. He plans to block off the airflow about a foot off the ground with a 2x4 framed into the closet walls. This does not seem like a good idea to me. Doesnt he need to protect the drywall from moisture? Or insulate the interior of the closet wall?
A vent isn't hard to extend. Any decent contractor could extend your current vent to closet wall. I am assuming this is the outside of the closet too - you don't ever put a vent in the inside of a closet and not even sure that is code. Anyway you need to part ways with this contractor if you can. If he even thinks about telling you something that dumb then who knows what he is doing when you aren't watching.
According to this reference:
using stud space as a supply duct is not permitted.