All of the major roads have guards. My guess is that (a) they use less well known roads, (b) they pay off the guards, or (c) they come in by water; but I have really no idea. Obviously I'm not expecting, "Well, when I was poaching radioactive horses . . ." but I'm hoping that someone might have an educated guess.
Setting is near future. I've looked at "Radioactive Wolves," a documentary on the zone's wolf population, and Googled variations on "Chernobyl poaching," but all I've got is that the horses are being poached, not how it happens. I wasn't expecting a definitive answer--if they knew how the poachers were getting in, they'd be able to stop them--but I was hoping for, again, an educated guess.