A winter tent will do a better job of keeping out wind or wind-blown snow by having fabric where a three season tent has bug netting, but this will not do a very efficient job of keeping the air inside of the tent from reaching the same temp as the air temp outside the tent. Yes, some of your body heat will be trapped inside if the air is still and this will have some effect, but it is unlikely to make as much of a difference as you seem to want.

Winter tents are not designed so much for warmth as for sturdiness in high winds or under heavy snow loads.