Do all the old mods still work with the SE or are there a certain series of mods that would not function?

No, none of the "old" mods work. All mods need conversion to new esp format at least. Some (such as those using SKSE) will take a lot longer than others. Some, where the author has gone without leaving permission, will never get converted.

Gotcha, so maybe consider holding off for a few months and see which gets converted... would it be fairly easy to convert some existing mods myself for private use?

Quite a few mods have been already converted. Only a few people have have access to the CK since it is in Beta.

SKSE will likely take quite some time to be made and be in a state as it is now for the 32 bit version. Also SkyUI might not be coming to the Special Edition.

I personally prefer the Special Edition over the 32 bit version.

You can try the special edition since it is a separate game and maybe you will like it even with the few mods.

But the chances have gone way up since it was discovered that the earlier versions without SKSE requirement work just fine with SE. All SkyUI seems to need is SKSE and someone just port it to SE.

Hopefully I will not be forced to use it again(Since some mods needed it) since I did not like the UI changes even SkyUI away still had a few leftovers from the UI changes. The only thing I liked about SkyUI was the MCM.

http://afkmods.iguanadons.net/index.php?/topic/4633-skyrim-se-things-to-know-when-converting-standard-mods-to-sse/

Also the CK is public now. The beta is over.