The Golan Heights has some decent accommodation options. Because the Hermon Mount is the only mountain in Israel with a snowy peak, the prices in winter are not necessarily lower than those in summer.
There is only one hostel in the Golan and it is really great (although very far north) – the Golan Heights is located in a village called Odem. A great place for nature lovers (+18 only!).
In the southern part of the Golan there are plenty of places offering beautiful views of the Sea of Galilee. I like to recommend Ramot Resort, The White Chalet View in Ramot and Peace Vista in Kfar Haruv.
In the northern part of the Golan Heights there are two places I like to recommend: Merom Golan and Kibbutz Ortal, which is still a communal kibbutz as well as being a lovely place to stay that offers great value for money.