Livy ~ I do believe you are correct on the first one as A. ludoviciana. In some reading I also found it listed with a common name as Estafiata which would be what I was told it was when I acquired it.
On the second, I am going to say it is not A. frigida. Sadly I don't have a good, full view photo of the plant. This plants' posture is tall all graceful. The branches splay out from a central base, more shrub like.
The first Artemesia sends out runners and pops up all over. The second one does not seem to have that same habit and although I haven't tried yet, I believe it would root easily from cuttings.
Thanks for helping solve 50%!