All the hotels in Tibet have hot running water for 24 hours. Some hotel may have taken some time to get hot water in the shower due to poorer infrastructure and the water pressure. But in the wintertime, you might find it harder to get the hot water in the shower due to the cold climate and also due to less tourist.

But the guest house in Shelkar, Everest Base camp tent guest house, guest house in Namtso and Western Tibet towards Kailash region, In most case does not have running water and even toilet in the room. You will have to use public toilets.