Llanasa and Gwaenysgor are lovely to ride around. If you drive up the hill by Graig Park you end up at a small crossroads and riding out from there you can head to either place nice long hacks or short ones and the roads aren't bad at all
You could also hack on the beech in Rhyl or Kinmel Bay
If you wanted to go for a nice ride without seeing cars you could go to Mostyn Farm Ride, not too far to go and it's up to you whether you want to do any jumps but these a little river to go through too which could be good experience for your horse
Some nice hacking in St Asaph near Llanerch Equestrian too if that's not too far from you?