Do Army Enlisted Soldiers wear this with there dress uniform or only Officers?

It's a Dress Blue hat. You wear it with your Dress Blues. There are not a lot of occasions when soldiers wear their Dress blues. I bought a hat just like this, the old one that went with my dress blues and I wore it a total of 1 time at the Dining in for ANCOC. You won't see folks walking around in those hats on a normal daily basis because it is for a "dress" uniform and most folks wear their duty uniform or best case scenario Class B's if they must. Otherwise you will see folks like the Honor Guard or those guarding the tomb of the unknown soldier where Dress blues are their daily uniform along with that cap. Officers will have one similar but the bill is adorned with golden braided leaves and basically just has more crap all over it. So in answer to your question for the larger majority of folks it is worn on special occasions that call for the Dress Blues (Dining In, Dining out, maybe a ceremony here and there which is even more rare) if you own them. Often folks just wear Class A's with the beret until later when purchasing Dress blues becomes more suitable as you progress in rank.