Maybe... it depends how well you want your brass to fit the chamber.
Be advised... the .358 Win sizing die DOES NOT have the same shoulder dimensions as a .358 Hoosier - it will be smaller than .358 Hoosier specs; .358 Win brass being longer and having the same taper there is no way around this fact. Also, after cutting 0.2" off a .358 Win sizing die, the base of your .358 Hooser brass will also be forced into a smaller dimension than .358 Hoosier specs. Many many posts were spent arguing this topic and 6mm Shoot did it anyway. To save $100.
Will it fit? Yes, I suppose. But you are working your brass more than necessary.
If you go this route, I would also get a .358 Win neck sizer die (unfortunately Lee Collet Dies aren't listed for the .358 Winchester, so there goes the cheap option) and cut 0.2" off that one too. At least then you can fire form the brass to fit the chamber, reduce the amount you are working the brass, and probably improve accuracy while you are at it.
I already have plenty of 358 Hoosier brass, could I use a 358 Winchester seater die to reload them?