Both DD and DS refuse to sleep under sheets and blankets so I have invested in snugtime sleep suits. They are like sleeping bags but have the legs and arms like a normal onesie. My kids would get tangled in sleeping bags and they hated them but love these suits. They can move around like normal without getting tangled and then as I'm heading off to bed I would cover them with a blanket. The house we lived in when DD was born was like an iceicle in winter and she was as warm as toast.
The snug time sleep suits are a bit pricey but I got some off ebay. Good luck.