Clip and check the cross section of the cane. If it is brown or black all the way through the cane is dead. If it is white or cream, with an ultra thin green layer just inside the bark, it's alive, alive!

Thank you!..Quick & easy!
I clipped one. The center is light brown with no sign of a green layer. I'll clip the rest this afternoon.

Let the canes with new foliage bloom before pruning. Those canes with no foliage on the lower portion can be cut back to 12 inchs or so to promote growth from the lower portion.
In our growing zone, Don Juan is not a good choice. It is very tender and an extremly cold winter will result in a dead Don Juan no matter what winter protection you provide.
although not as fragrant, Dublin Bay is a hardy red and a better choice for zone 5. Mine stayed green over more than two thirds of the bush.
Don't fret the loss of canes. Repeat blooming roses bloom on new wood. Pruning promotes new wood. Aside from a shorter climber for awhile, the bush will recover and grow quite large before next winter when the exercise will begin again.

Thanks for the input, Karl. I'm tempted to buy 2 hardier climbers this year & switch out 2 of the Don Juan's. I'll definitely look into Dublin Bay. Would you be able to throw more suggestions on hardy climbers seeing as we live in the same area? I'd appreciate it. :)