yes you def need to invest in a couple of warm sleeping bags.
we have got 2 so there is one ready in case there are any nappy accidents or spews etc.
i love DS's ones - we got the 2.5 tog (weight of fabric) from The Dream Bag website, they are very similar to the original grobags but half the price. DS sleeps wonderfully in it, and we don't have to worry about him getting cold or getting his face under a blanket.
the bags are sleeveless though, so on really cold nights (it has been 2 degrees a few nights here recently) we have just put him in his longsleeved jumpsuit, and 2 pj tops. he slept in for ages the mornings we had him in that!