A horizontal fly opens side-to-side instead of up-and-down, and it lies flatter against your body than a traditional vertical fly. The main benefit is reduced bulk under your mid and outer layers—which matters when you're already stacking a baselayer, insulating layer, and ski pant over it. Less bunching at the front means a smoother, more comfortable fit throughout the day.
You'll mostly find horizontal flies on performance-oriented base layers designed for active use. If you're layering tight and want the cleanest possible interface between garments, it's a solid choice. The trade-off is that some guys find it less intuitive to use than a standard vertical fly—it's just a different motion.
It's a small detail, but if you're particular about eliminating unnecessary bulk under your kit, it's worth seeking out. If you don't care about that, a traditional vertical fly works perfectly fine.