Tanner Roark starts against the Astros and Chris Young against the Braves.
Ryan Zimmerman stayed home and continued his preparation to play first base for the first time.
Rivero is optioned to Class AA Harrisburg and Cole is reassigned to minor league camp.
The Nationals' starter, dealing with elbow inflammation, threw from flat ground on Wednesday and said he'd be ready to go when the games count.
Stephen Strasburg appears to be the safe assumption, but Matt Williams says he has not ruled out Jordan Zimmermann starting opening day.
Jordan Zimmermann retired all 12 batters he faced against a strong Yankees lineup.
After the starter played catch this morning, the Nationals think he will be able to take his first turn in the rotation.
The Nationals closer insists that he feels fine during spring training and that he's not worried about the seven runs he has allowed in two games.
The right-handed starter played catch on Tuesday morning for the first time since feeling tightness in his elbow.
Jordan Zimmermann will face a strong Yankees lineup in his third start of spring training.