My Mare has had hicups before apparently a few times normally when the grass is wet - I've never seen it for myself but the girls on the yard rang me as they were really worried by the time I got there it had stopped! This was last autumn and shes fine a year later so I wouldn't worry about it to much - maybe if you went for a gentle strole it would tike her mind off them and it would go away - but I would try making her jump lol !
If the horse seems in pain or distressed (respiration up, temperature up) then it could be a front of stomach colic and this is soemthing thatt can drag on for a few days before becoming serious. If it keeps going for more than half an hour or horse distressed - best to call bet. Buscopan sorts it out.
My mare hiccoughs, Vets didn't believe it until they witnessed it!
As SMID says it has always been a precursor to colic with my mare.
After four episodes she was scoped and found to have Gastric Ulcers. They have been treated and have cleared. The only time she does it now is if she is a bit nervous, ie I am late bringing her in, or I have changed her routine.
It's halfway between a hiccough and a windsuck really. She has been known to actually burp during colic though.