My old greyhound had to have two housecoats at night as he got so cold and he refused to leave the house without his walking coat (plus layers underneath if very cold). They feel the cold because they don't have double layer fur like most dogs, plus they tend to be bald underneath and skinny so not well insulated.
All four of our greyhounds are still wearing their fleece housecoats at night. It's an exceptionally cold spring this year, and we've been seeing ice on puddles and our garden pond until early this week. Even in a modern centrally heated house, overnight temperatures will get pretty chilly. It's particularly important if your grey is elderly. The only other option is for them to be on or in the bed with you and ours are quite partial to this too!
Do you cover your grey up at night before you go to bed?? If so what with & are they still covered up when you come down in the morning?? I think our old girl needs covering up but dh thinks I've lost the plot!! But they do feel the cold more then other dogs