There are loads of them but unfortunately you only tend to find out about them from word of mouth.
I know there is a place called Fron Farm (caravan park) which I have previously been to look at but didn't have spaces when i got my lad and does look lovely so they may be worth a try and have fantastic hacking on the doorstep. The other 2 places where we keep our horses don't have spaces at the moment.
The other place where people tend to advertise and I hope I don't get in trouble for this is NorthWalesHorse.
The Whitehouse by PenyFord (can't remember exactly how you spell it) has a notice board that people tend to put ads on for places or Acre house saddlery.
The other place I know that did have spaces was Hunters horses. They do have a website but I can't remember what it is. never been to visit them but it does look nice on the website. If you Pm me I can send you their phone number