Yes. I recently spent over a year living off-grid and used a smaller tent inside a larger one to conserve heat in the smaller one. The inner tent was my sleeping area while the extra space inside the outer tent was used for storing non-essential gear and items which needed to be protected from exposure to the elements. For short camping trips, using 2 tents is not very practical, and you'd probably do better to just put a blanket or other insulating cover over a single tent.
You will need to use some sort of barrier between the tent poles and the floor of the larger tent, such as bits of cloth or even styrofoam pressed over the pole tips. I used a tarp with an emergency blanket laid over it and set up on top of the blanket.
The outer tent does not provide a great deal of insulation, but it does reduce air-flow between the outside world and the smaller tent. This can greatly reduce heat loss, especially on a wet or windy day. Since your body puts off heat naturally and the inner tent retains heat more efficiently, it can become toasty inside the inner tent. If you have a camp heater, it can be used in the outer tent to keep temperatures up without making the inner tent stuffy or over-warm.
Another trick for conserving heat is to put a blanket on the floor of the tent (even if you are only using a single tent) to act as a barrier between the ground and your sleeping space.