Is in contact with about 55 to 60 degree soil. This means that there is only a 10 to 15 degree difference between the floor temperature and the room temperature assuming you keep the basement room at 70 degrees.
The bottom line is you need very little R factor (insulating value) to make your floor feel warm.
If I were you, I would conserve your headroom and go ahead and install a 5/8 inch rebond carpet pad, then your carpet over it. This will give you plenty of insulating value (more than the 1/2 inch osb) and be a much less complicated installation.