We investigate the possibility of having horizons inside various classical field configurations. Using the implicit function theorem, we show that models satisfying a certian set of criteria allow for (at least) small horizons within extended matter fields. Gauge and global monopoles and Skyrmions satisfy these criteria. Q balls and boson stars are examples which do not and can be shown not to allow for horizons. In examples that do allow for horizons, we show how standard "no hair" arguments are avoided.