shepherd mentioned:

I know hybrid teas and many other roses can not be propagated successfully
from cuttings,

Where in the world did you get that crazy idea?

You can propagate the vast majority of roses of whatever kind from
cuttings. Some are easier than others and a few are downright finiky,
but they are very few.

Finiky.... I like that word...

but is it possible to use cuttings from climbing roses for
propagating?

Yowza. Be forewarned though that it is going to take you 2 years to
catch up to the plant size you can buy in the store today.

Because of the time and effort involved, I myself limit propagating of
cuttings to varieties that you can't get elsewhere. The cuttings I am
looking to start this year a

Maestro
Cimarosa
Peppermint Swirl
My Choice and
Quaker Star

Can't find these anywhere, so I am going to politely ask for cuttings
from the San Jose Heritage Rose Garden when I visit there at the end
of April.

Bob Bauer
Moving 20 roses (some HUGE) and giving away 12 more in the next 3
days. This is too much like work! heh heh