There'll be 90 players on the roster for most of training camp.
In news not related to the draft, the NFL announced that the offseason roster limit will be expanded from 80 to 90 players, effective 4:00 pm ET yesterday. The move will provide teams with greater roster flexibility and allow more players to be developed and evaluated.
Per the NFL, the 90-player roster limit includes players on the active, inactive, practice squad, and exempt lists, and the following reserve lists: injured, physically unable to perform, non-football illness, non-football injury, suspended (for less than one year), future, drafted-unsigned, exclusive rights, first refusal rights, unrestricted free agents with an individually negotiated right of first refusal, franchise, and transition.
As in previous non-lockout seasons the first roster reduction will happen at 4:00 PM ET on the Tuesday, August 28 following preseason week 3, when rosters will have to be trimmed to 75 players. And because the Cowboys and Giants are opening on a Wednesday this year instead of the usual opening day on a Thursday, the final roster reduction to 53 players has also been moved up one day and will now happen at 9:00 PM ET on Friday, August 31 of preseason week 4.
The Cowboys currently have 60 players on the roster, so even with the eight or so draft picks they'll pick this week, they'll still have ample room to bring in college free agents and other possible additions to the team.