We see several times where Jadzia was surprised by a memory Dax had, most notably of Joran Dax (whose existence proved that the symbiotes were compatible with most Trills, not just the selected few).
The existence of the Zhian'tara in the episode "Facets" more or less proves the memories are limited. Why have a ceremony to reminisce with old hosts if you have all their memories?
We also see from the episode "Field of Fire" (where Ezri Dax pulls Joran out into her consciousness) that hosts can "bury" prior hosts to some extent, which implies some control over memories as well (screenplay, emphasis mine)
EZRI: Chzui vok Ezri sheyhal bashar. I'nora ja'kala vok.
JORAN: I can't tell you how much I've enjoyed our time together.
EZRI: Zheem Dax nah sass eye ahn. D'za oo bah zheest. Joran rhee jehr hey dah
JORAN: You won't be able to forget me or bury me as deeply as Curzon or Jadzia did.
EZRI: I know.
JORAN: I'm part of you now. As much as Audrid, Torias, any of them.
EZRI: I'll have to be careful. Tu Dax noh zhian 'vok j'zui.
(Joran fades away.)
EZRI: Joran rhem tanas Ezri.