You ask if the cold spring should be included in the "spring load case".
There are (at least) two spring sizing load cases: 1) collecting the load to be carried by the spring and 2) the spring travel from installed to operating. I cannot respond directly to your question without knowing your "spring load case" reference.
I think the biggest concern, here, is whether or not there is a vertical component to your cold spring. A vertical component may greatly alter the calculated weight distribution in 1) above and the calculated travel in 2) above.
My quick guess - exclude cold spring from all hanger sizing load cases but include it in all post-selection load cases. And then confirm proper spring loads and displacements in those post-selection load cases.