If you push yourself too much even when you are stretched and warmed up you can pull a muscle, but I don't think it's possible to break anything. Splits is a stretch, so as long as you aren't over stretching it's not dangerous. If you warm up and strech the rest of your body before though you will probably go down farther.
Yes its dangerous! I am super flexible (can be quite annoying at times!) and while I can easily do splits without warming up you can still easily hurt yourself and I learnt that the hard way! I just went straight into splits like I used to do almost everyday and I felt this really painful pop. Turned out I ripped my hamstring! I was off gym for ages and could barely lift my leg past horizontal! Now I stretch every time before I do splits!
DO NOT DO IT! I DID IT A COUPLE OF MONTHS AGO AND I PULLED A MUSCLE IN MY LEG! I STILL CANNOT GO AS FAR DOWN IN MY SPLITS AS I USED TO ON THAT LEG! I also couln't do alot of stuff at gymnastics just don't try it.