I don't have a lot of experience with a tipi, but I do know that one that is not set up right, and/or an owner who does not know how to regulate the fire or the smoke flaps can literally smoke the occupants out.
Don't ask how I know, and it wasn't my lodge.
Depending on gear, it would probably require a minimum of a 16 foot diameter lodge to house four and gear comfortably. A 20 footer will provide MUCH more room.
A 12X16 wall tent provides 192 sqare feet of usable space. A 16 foot lodge, provides 201 square feet of FLOOR space. The problem lies in the fact that the walls of the tipi slope inward shrinking that usable floor space rather quickly.
Do you plan to sleep on the ground or use cots?
IS you cook gear in square, wooden "camp boxes"?
What about cooking and eating tables? Chairs?
All of these things will reduce the usable floor space of a lodge rather quickly.
Also, if the nights are cold, how do you plan to keep the fire going? With a wood stove, all ya gotta do is get a fire going and stoke it up, close off the damper, and you're good to go for most of the night.
With an open fire in the lodge, someone has to replenish the fire wood on a regular basis. The problem is, most folks tend to wake up cold and pull the covers over their head rather than get up in freezing weather to stoke the fire. It's hard to get warm again after running around a cold lodge, so the person who elects to stoke the fire doesn't get much sleep.
Another consideration is the fire hazard. I've seen far more lodges go up in flames than wall tents as someone accidently kicks a flamable object into fire, or by the fire spitting hot sparks onto clothing and bedding.
I would suggest laying out a 12X16 area using rope for the perimiter and place everyones gear in the the roped area. Leave enough room for the stove and firewood.
How much room so you have? Is it enough to live comfortably for the duration of the hunt?
Do the same using a 14 foot, or so, circle to simulate the usable floor space in a 16 foot lodge.
Which provides the most usable living space?
J.D.