As a recumbent rider, meeting a dobbin coming towards me, it's a no brainer to stop sit up and speak to the rider. Dobbin and his four legged mates have no idea what a recumbent is and will shy and skitter on siting me on the move.
Catching one is more of a problem, I try a toot of my squeeze bulb horn from very far back, but this is usually not heard, as I get within calling range I call out:- 'Am I OK to come through?' Then the fun starts, some riders will wave me on and I go to the edge of the road while putting on a bit of a spurt. Others will ask me to wait and go into a field, turn off or in one case dismount and hold the horse's head while talking to it.
I keep up a chatter about the weather, the price of fish or anything else so the horse knows I'm human(ish).
The last thing any of us wants is the horse hitting us and the second last thing we want is the rider getting unseated so I'm ultra cautious around them. An equestrian friend once told me the secret about horses, she said:- 'Remember that they are all crackers!' Another rider I spoke to stunned me by telling me that his Hunter, which he often rides on roads, is terrified of concrete!