Which party assigns delegates in a "winner take all fashion" during the Iowa Caucus

The Republican Party.

In order for a Democratic candidate to win delegate nomination in the Iowa Caucus, they must secure a specific number of votes in proportional allocation; however the Rebublican party delegates will be assigned in a winner-takes-all fashion, which does not take into consideration, the voting patterns of the various regions of the state, simply relying on voting of the participants (which is also done in secret).