When I pour water into the fill tank on top of motor it will run out some where on the back of the engine while it is cold and no pressure. I have taken it to the dealer and they say Ineed to replace the egr cooler and the head gasket. My question is why the water is coming straight out of the fill tank with no pressure if this is the problem.I have never seen it leak when it is hot.  

6.0 or 7.3??  

it could be the resovoir, some of the newer trucks have the pressurized ones and can crack, but it could be the head gasket they are pretty notorious for popping  

if it is the head gasket make sure yuo have them put studs in it not the weak ass head bolts the used. they were especially weak in the 03-05 models as they used m-8 head bolts where in the 06 models some geniuos decided to run M-10's they are a little better but to be on the safe side STUD it its the best thing you could do for that engine.  im guessin by you talking about the egr valve its a 6.0 bein that 7.3's had no egr. also elitedieseleng.com makes a block off plate for the egr on 03-04 6.0;s and i think it only costs like 30 or 40 bucks. and that will eliminate the problems with the egr if you start running a programmer and your engine will run a lot cooler as well and put less pressure on the heads/gaskets  

but how you mentioned it only happened while it was cold i would look into the resevoir as stkdram mentioned because it doesnt make sense it doesnt do it when its hot...