I have a query.

If cold spring is used in piping & spring hanger is also used, then whether
1. Spring load case should include cold spring or not?
2. spring should be designed for a or b case ?
where
a. ope case+without temp+cold spring
b. sustained case without cold spring

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.

Thanks Dave for your response.

Now I have 3 post load cases after hanger design as below:
1. OPE (W+T1+P1+H+U1+CS)
2. OPE (W+P1+H+U1+CS)
3. Sus (W+P1+H+U1)

Now there is a huge difference in vertical displacement because of CS in all the above 3 cases.
My query is what is the perfect way to design the Spring for load & travel in this case?

If your springs were sized with no CS and there are significant CS effects in the vertical direction around these springs you will have to consider (as you suggest) a few adjustments to your analysis.
Think of it this way, you have the right spring you just have to adjust it's vertical position. Your springs were set with no CS. Picture your springs in place with that last CS gap still open. When you close the gap, the springs may be pulled up or down. Ideally, you would reset the springs by adjusting their vertical position to get everything back to the proper position and hanger load (e.g., by adjusting a turnbuckle). It is this vertical adjustment that you should include in your analysis.
I would run an analysis to see what this delta Y (Y is vertical) is at each hanger point. I would guess that a CS load case, alone, will give you these values. Take these Y displacements and add them as displacement load set on CNodes defined for your hangers. Then, include this displacement set in all analyses performed after the hangers are installed.