A wood burning fireplace should not make your house any colder unless you have a draft problem with your chimney.
When you're using your wood burning fireplace the house and room you're in should get warmer which means you won't have to run your regular furnace as often which can save you money on your heating bills.
However if you're trying to heat your home with just a wood burning fireplace then your entire house may not get warm enough.
Wood burning fireplaces are not very efficient at heating a house but they are nice and most of the heat actually does end up going up the chimney instead of in the room.
If you want to heat your home with wood you really should look into installing a fireplace insert for your fireplace.
The wood burning fireplace insert will throw out more heat and not allow much of the heat to escape through the chimney.
Or use a regular enclosed wood burning stove which is even better at heating your home using wood.