We did see some people with dogs but none in main building just give them a call and they are so nice and helpful they will let you know
The rooms are chalet style and separate from the main hotel so you would probably be able to keep them in there. But we only went for the restaurant and I don't think they would allow them in there. It might be best to call them to find out for sure.
Get quick answers from Burn How Restaurant & lounge Bar staff and past visitors.