as said I am getting water into my hydraulic trim system. The oil is milky. I rebuilt both cylinders and nothing is leaking on the back of the boat. The reservoir is overflowing and making a mess.
Is it possible for the hoses to let water into the system but not leak oil?

one of the seals on the ram rod must be bad,ones for pressure out and other for keeping water out.keeping water out one is bad,only way it could happen.

I rebuilt both of them. I replaced ALL of the seals and O rings. I even used 2000 wet/dry sand paper on the rams so as to polish them up nicely.

Do you have a steering cooler?

I agree with sut 30 , the rod wiper on one of the cylinders is pulling water in under trim down . Are the trim rams nicked , gouged or damaged ? Ive also seen the Cylinder end caps pull in water under trim down while in the water. Test for leaks by putting a block of wood between the drive and transom or trailer , and trim down against the wood. Thats the only way to put pressure on the trim down circuit, and create a leak .

were the seals identical,duel lip?

Just adding possible other areas. You have a Hydraulic manifold under the transom assembly that your lines connect to. I would look deeply into all of that area / lines plus depending what exactly you have there also can be a gasket and a rubber seal. There can be anodic block installed over the hydraulic manifold.

Also make sure your trim reservoir cap is the one that vents from the internal threads or the newer style in which is the best cap to have instead the old cap that had a small hole in the top of it. That hole in the top of the yellow cap allowed water in from drainage off the swim deck area down onto the top of the yellow cap, then of course thru the small hole down into the trim reservoir.

Also there is hydraulic test gauge that will allow you test pressures at the manifold and this will also see if that is your leak area on top of.

In order to draw in water it would have to suck in water when I am trimming up. Pump pushes oil into the transom end of ram and sucks oil out of the prop end. When trimming down it pushes oil into the prop end and sucks oil out of the transom end. I have the stock Merc cooler with steering oil cooler built in. I don't have the anodic block installed since my drive hits it because of the negative trim increase I have. ( I tapped and plugged the hole ) Is it possible for a hose to allow water in without leaking oil???

If water is leaking in then quite likely oil is leaking out. You have nothing to lose by putting some UV dye in the system to see if you can spot a leak. That stuff has been a miracle for me chasing down fluid leaks in my 20 year old boat.