One factor to consider, that I haven't seen here (but could be on account of many answers): On a steel string the tuning posts are vastly different than on a classical guitar. You will have difficulty tuning a nylon string using a steel string post. (I once tried to put steel string tuning posts on a classical guitar and the result was almost useless.)
Also, I have seen this in the answers, but to reinforce: There are many good acoustic guitars designed to feel like and play like a steel string, but are designed for nylon strings. That is your best option.
Also, as a classical guitarist, in my experience the classical strings that have the ball ends suck. (to use a technical term.) In other words, they just do not sound good or feel right when compared to good brand name classical guitar strings.
Probably the best version of your idea is to get hard tension classical guitar strings and tie knots on the ends, since if they are any good they wont have those ball things. As others have said, silk and steel are also worth investigating. I never tried them myself, but when working at a guitar store, they seemed to sell reasonably well.
It is possible to put nylon strings on a steel string guitar as others have said. It is likely to sound terrible. It probably wont hurt the guitar. It is possible. Acoustic guitars with floating bridges would have a problem with nylon strings. The tension would not be enough to hold the bridge in place. You are likely to get allot of fret buzz.