There are differences between subscribed, installed and activated mods.
If You used only mods from the Steam Workshop (subscription) and all mods were activated, it is easy since Steam should automatically install all subscribed mods on your new PC. Maybe you will have to activate them.
If you use mods from other sources, you will have to install them manually.
If your savegame used only a selection of activated mods, you should make a list which mods were used and activate only those mods on your new PC before loading the savegame.