Most hills are fairly dog friendly, you just have to make sure you yourself are aware of the risks and dangers with dogs on the hills. I have two that I take along regularly and they've done pretty much all the hills that I have - not a huge number but a good few.
Get the dog on a lead when there are sheep about is the main thing, especially when there are lambs as it's not necessarily the dog bothering the sheep but they might try to protect the lambs and hurt the dog if it gets too close.
Dogs are decent climbers / scramblers but be aware of sharp drops and keep the dog well away from them if you can, they are usually pretty careful but if they get excited they could go over.
Last bit of advice is make sure your car is well protected for when you get back to it, they can get very wet and very dirty, learned that one the hard way
