Most horse owners are really cool... Throw out a
SINCERE compliment about "the beautiful horse" and they usually melt, even if they were grumpy to start. Same with dog owners... They can't help but be polite if you
GENUINELY CONFIDE about how beautiful Fido is.
Mr. Stubborn Approach nails it... The horses have the right of way, but on top of that, you don't want to surprise them. Make sure they know you're there, and 99 times out of a 100, the owner will quickly make the situation safe to pass.
When you meet the 1 exception to the rule, you'll know it. And nothing you do will make the situation better.