I have heard many times that Fort Dawnguard is a player residence, but I've never noticed any bed, chest or general area that was obviously 'mine'. I really don't want to have to get Breezehome, again.
There is a small "corner" upstairs that is yours, but that is all. I usually go and get the house in Morthal and build it to suit my needs and add the furniture and stuff to suit my needs. But the corner you get in Fort Dawnguard, is about as large as the downstairs in Breezehome. Hope that helps.