I dont know whether to start it with my level 65 or start a new character.

What would you guys recomend?

It's intended to provide a challenge to high level characters.

Keep working on yours to get him to at least 80. Then go to Solstheim.

I'd say use your level 65 just because lower level characters won't stand a chance.

So I shouldn't even attempt it at lvl 35? Can I at least vacation there?

Oh I started it on a character that was around lv35 actually. Found it difficult but not impossible.