Getty Dallas Cowboys HC Brian Schottenheimer. The Dallas Cowboys might be out for blood in the 2026 NFL draft. Armed with 2 1st round picks at No. 12 and No. 20, the Cowboys are 1 of several teams in the market for trading up into the Top 10 — specifically to get the No. 4 overall pick and screw the New York Giants with the No. 5 overall pick. The 1st round of the draft is on April 23 in Pittsburgh. “There’s a belief among teams at the top of the draft that the Cowboys , who have picks at #12