From a technical perspective, two clients make little sense. Why would any developer go through the trouble of maintaining two separate code bases for players playing essentially the same game together, with one part of the players being allowed to use features others can't. Both clients would have to be constantly updated, as exclusive features would still affect both clients.
A practical example: A Horizons player carries a SRV on their ship. A season one player scans that player with a cargo scanner. How are they going to see what the Horizons player carries, if they were in a client that didn't know anything about any Horizons content? Their client would have to be updated to support Horizons content and base features, like crafted equipment.
It's so much easier to maintain a single client that requests the purchases of each individual player from a server and then allows them to use certain features based on a "pay-wall", rather than having to maintain two separate clients and keep them compatible.
The most likely scenario then, is that everybody will receive the "2.0" update, but season one players will only be able to use a subset of the new features as determined by Frontier. Any other approach to implementing Horizons would greatly surprise me, although it remains to be seen how the versioning will be continued if "1.5" and "2.0" will indeed be simultaneously released, hinted(?) at.