We see snakes all the time in the warmer months. Never had a horse have an issue with them, kings, gophers or rattlers. Most move off the trail when they feel us coming, or they shoot off into the brush for cover. I've only ever had two times when a snake wouldn't move out of the way. Both times they were rattlers.
First time, we were riding on a wider fire road type trail. Rattler was stretched across, sunning himself. We waited for a bit for him to move on and when he didn't, I dismounted (from a seriously safe distance!), and tossed some rocks near him to try and 'encourage' him to move on. Nothing hit him, but dude wasn't moving. He decided to curl up and get in striking position (obviously he felt threatened). Then he went all Cobra on me, raised up and started snaking towards me a foot off the ground. Never seen one do that before. We decided he won, and backtracked to a different trail to get home.
Other time, two rattlers doing the deed in the middle of the trail. Never seen snake mating rituals before and it was kind of fascinating. It went on FOREVER. So long that two other horse groups, a set of mountain bikers and some hikers all surrounded the lovers on both sides of the trail, watching NatGeo in HD. Honestly, it was kinda cool to see.
One thing I have always been taught is to carry two sections of new garden hose, cleaned in ziplock in my saddle bags. Because rattlers around here aren't usually aggressive, a lot of snake bites end up being on the horse's nose while they are grazing or shuffling around in the bushes. The hoses go in their nostrils to keep the airways open when the nose swells up, until you can get steroids in the horse.
I've never done it and never seen it personally, but I've always carried them just in case.