I bought a guitar which has a classical guitar bridge but a steel guitar tuning pegs and strung with steel strings. I'm wondering if I could replace the steel strings with nylon strings.
Usually it's the other way! No reason why this can't be achieved, but the tension on the strings will be less, affecting, possibly, the relief on the neck. In other words, the neck may well straighten out, and this can cause the strings to be too close to the fingerboard, thus rattling. If the neck has a truss rod and the bridge is adjustable, all will be well.You may or may not like the resulting sound, though, as it will be quite different.
Guitars designed specifically for nylon strings typically do not have a truss rod to compensate for string tension. If your guitar is designed for steel strings, it should have an adjustable truss rod visible either through the sound hold in the neck block or under a plate where the headstock joins the neck. The truss rod can be adjusted to allow the proper relief to keep the strings from being too close to the frets which would cause them to buzz or not play at all. Without a truss rod, the tension of the steel strings would cause the neck to bow and the strings to be too high off the fret board in the middle of the fret board. Nylon strings do not create the same amount of tension on the neck, thus many guitars designed specifically for nylon strings, will not have a truss rod. Going from steel strings to nylon strings will create less tension on the neck and so would not hurt the guitar. But nylon strings will not sound the same as steel strings. Also, nylon strings tend to be larger diameter and if the string slots in the nut (at base of headstock) are cut for steel strings, the nylon strings may not seat properly in the slots. A qualified luthier or guitar tech can use a nut file to enlarge the slots should you desire to permanently convert to nylon strings. Or you can replace the nut.