For winter camping I use my smaller tent to maximize heat retention. And yes, always throw down a ground sheet or at least a bed of spruce or cedar boughs if available. You can use pine too, but the pine pitch gets all over your tent, so if you have to use trees, go for one of the other species first if possible.
If you pitch your tent in a good sheltered area and have decent gear, you can camp in some surprisingly cold weather and stay pretty comfortable. I build a long, narrow fire to radiate heat in a wider area, and the tents are never down-slope from the fire. We will sometimes also clear the snow a bit and pile it up to build a wind block with it. You can use sticks and branches for this purpose too.
Edit: I should add too that we also throw the tree boughs around the campsite on the ground to provide some traction against the ice. When the fire melts the snow and it re-freezes it can get very slick, so the tree boughs (small ones) scattered around the camp area helps to prevent falls and injuries.
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