The Fulbright Program is administered by cooperating organizations such as the Institute of International Education and operates in over 160 countries around the world. The Bureau of Educational and Cultural Affairs of the U.S. Department of State sponsors the Fulbright Program and receives funding from the United States Congress via annual appropriation bills. Additional direct and in-kind support comes from partner governments, foundations, corporations, and host institutions both in and outside the U.S. In 49 countries, a bi-national Fulbright Commission administers and oversees the Fulbright Program. In countries that have an active program but no Fulbright Commission, the Public Affairs Section of the U.S. embassy oversees the Fulbright Program. More than 370,000 people have participated in the program since it began; 62 Fulbright alumni have won Nobel Prizes; 88 have won Pulitzer Prizes.
https://en.wikipedia.org/wiki/Fulbright_Program
Its probably illegal for them to cancel it, but it would take a long time in the courts to establish that. Trump hates these incredibly smart people who get Fulbright scholarships because they never vote for him.