I was just at Lake Cumberland over the 4th of July, and I can guarantee that they did not care at all that we were drinking on the boats. We rented the two largest houseboats available, and brought 25 partyballs and 20 cases of beer with us, not to mention the liquor. I don't remember seeing one boat that didn't have some type of alcohol being consumed.
Even when one of my friends got pulled over at 3:00am on his boat after drinking, all they did was a field sobriety test, and when he decently passed, they told him to go straight back to his houseboat and stay there for the night.
I would say the most crap we got was from the people at the docks because it was the first time the boats were ever being used and they were scared we were going to party a bit too much
Overall, i highly recommend going down there for a weekend.