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 usually stain or apply brushed or rolled on finishes inside. Spray finishes I do in the garage, but quickly, then I immediately bring things inside to dry in an isolated room (usually the master bedroom, which has an attached bathroom.) I leave the fan on in the bathroom, which pulls the fumes out. If you're spraying from rattlecans or a gun, it's important to keep the materials inside until you're ready to spray, or they'll go on strangely because they're cold and sluggish. Your compressor needs to be outside though or you'll get serious amounts of condensation in the air lines.