There are a few options for you...
1. Split your parts in Visualize. If you open a multibody part file in Visualize with only one color (or no colors) applied in SOLIDWORKS, all items will be in the same grouping. Click Project -> Model - Select Parts to Split. Click the part you would like to split, then choose 'Execute Split'. Do this as many times as needed.
*If you would like to group parts together, multi-select the items in the tree, then choose 'Create New Group'.
2. Apply appearances in SOLIDWORKS before opening in Visualize. Visualize will recognize the different colors applied in the part file and extract these automatically.
3. Save your bodies to a new assembly from within the SOLIDWORKS part file. We have an example of this at the link below...