Question: If you want to stain and varnish indoor wood furniture during the winter, how do you do it?

It's below freezing outdoors, but I don't want fumes to accumulate in the house.

Answer: 
In the past what I have done is to isolate 1 room, generally in the basement, increase the heat to that room and open the window while running a fan. In general, once I've closed the can and am only waiting for the piece to dry the fumes tend to get much less noticeable and I can start closing the window.

This method doesn't prevent fumes from reaching other rooms, since they can travel through the ducts or even under the door, and so on, but you can reduce those fumes by closing the house ducts to that room, putting a towel over registers/returns/bottom of door. 

With this method you'll want a heater for the room. I've used electric oil filled heaters but you'll just want to keep in mind that the fumes can be flammable, so keep your venting method running.
I have a huge problem with paint and stain fumes. I love these projects but the fumes really get to me. 

Today I found a good solution. I am very proud. Like said above, put the done woods in a closed room and close off the heater vent in that room. Use a fan and open a window. What I did was add a fragrance oil burning kit. The room will smell pleasant. 

Note: always wear protective glasses and mask when painting + staining. You will be less dizzy than me when you are done.