First off, we should wait that Mods on PS4 will work as intended, as it seems the PS4 is facing some complications on that matter!
Why ask this here? That would be better answered on the Nexus.
The game will be 64-bit and most mods should work as they are. SKSE and plugins using it will need to be updated.
Basically:
https://twitter.com/DCDeacon/status/743170497752371200
https://mobile.twitter.com/DCDeacon/status/743192238541307904
Since they'll be uploaded separately, with a different CK, I imagine the Nexus will need to create a secondary Skyrim directory specifically for the remastered version. Otherwise there will be considerable confusion with people trying to download/install incompatible/outdated mods. Or they could rtfm, I suppose.
Yeah. What a HUGE problem for people, right?
It may well be a better approach to have a separate SSE section on Nexus. We won't really know for sure though until we can assess mod compatibility ourselves in October.