He started 10 games out of 12 as a true freshman at free safety, tallying 61 tackles (3 for loss) and 2 passes defensed.

[3] On March 23, 2017, he participated at Louisiana Tech's pro day, along with Carlos Henderson, Trent Taylor, and 12 other prospects.

[4] At the conclusion of the pre-draft process, Woods was projected by NFL draft experts and scouts to be selected anywhere from the fourth to sixth rounds.

[10] Throughout training camp, Woods competed for a roster spot against Robert Blanton, Kavon Frazier, and Jameill Showers.

[11][12] Head coach Jason Garrett named him the backup free safety to Byron Jones to begin the regular season.

On September 25, Woods recorded three solo tackles and deflected a pass in the Cowboys' 28–17 victory at the Arizona Cardinals.

He recorded his first career tackle on the opening kickoff on Cardinals' running back Kerwynn Williams after a 21-yard kick return.

[16] In Week 11, Woods earned the starting strong safety job and recorded three combined tackles during a 38–14 win against the Washington Redskins.

In 2018, Byron Jones was moved to right cornerback and Woods was named the regular starter at free safety in the organized team activities.

He missed the first 2 contests of the season, with a hamstring injury he suffered in the preseason game against the Cincinnati Bengals and was replaced with Kavon Frazier.

If he's running full speed the whole time, it's just not possible, to be honest", which Woods maintained that it was taken out of context and that it was not indicative of the team's commitment or effort.