I love that Jameis Winston considers playing an exhibition game against the Yankees a greater accomplishment than winning the BCS title. I love that he wants to play baseball and football. I'm afraid, however, that is extremely unlikely.
It's not because he doesn't have the potential or desire or ability or anything like that. It's that he projects to be a pitcher. In football, he is currently a quarterback. To play both professionally, he would basically be throwing at (more or less) full force from early February (when pitchers and catchers report) through at least December with no time off.
Unless he plans to change positions in one of the sports, or his arm was built in the same factory as Mariano's, there is no way that is going to happen. Under that sort of constant throwing, his arm maybe holds up a year or two before he needs major surgery. No team would take that risk. No team would likely even ask Mr. Winston to take that risk.
As much as it would be throw-back cool to see Winston play in both the Major Leagues and the NFL, unless his role in one of those leagues doesn't involve throwing, there is no way that's going to happen.