As far as care, some sphynxs are more oily than others. Usually the oil is absorbed by the fur. I have to bath him once a week in soapless shampoo to clean off the oils and I also clean out his ears as they also build up. Both are are very easy especially the bath considering no hair to wash.
Oliver is not very oily. I do have a coat for him. I'll take a pic of him in it. He also gets under the covers during the day and sleeps to keep warm. I also bought a disc you warm in the mircrowave and I stick it under is bed. It stays warm all day!