My understanding of the question is Rahul wants to save the Solid Edge drawing to .DWG and wants to see the colors used from SE in the DWG. If yes, I am able to verify this.
My best guess and workaround is if the drawing elements are organised on layers in Solid Edge, then the Options wizard in DWG SaveAs dialog has a facility to map color based on layers.
This worked for me and that's the closest I am able to get based on my limited knowledge in this area.
1. This might involve some-rework and re-organization but CAD standards are always useful.
2. Nice to see someone doing some serious AEC stuff in SE Drafting
As @Tushar says...in the DWG save "Options" area, there is a check box that makes this all work like you need it to.....uncheck the "Do Width to Color Mapping" box, and click finish.
Design Manager Streetscape Ltd
Solid Edge ST10 [MP8] Classic [x3 seats]
Windows 10 - Quadro P2000
Testing: Solid Edge 2019
You will want to be looking at you SEACAD file. The wizard can be accessed by selecting save as DWG, then click options. Depending on how the colours were generated, and how you would like to present your drawing, you can either assign colours and linetypes to layers, or colour width mapping.