I think a lot of it depends on your room temp. I have figured out ways to split aquariums in 2 and still get proper heat distribution, but I know that if I don't have enough water flow that I will have major problems including cold spots and my heater only heating the water around it and then turning off before it gets a chance to heat the rest. My house is always fairly cool though, so if your house is always fairly warm then it's a different story ;) I don't know how you could filter it without multiple filters (at least 2-3 depending on how many sections you divide it into).
If you are going to do it, I would only split it into 4. I think that's a better space for each betta, and 1 less divider to worry about. There is also the issue of fish compatability. If you know your 4 are ok as neighbors then that's fine, but I have 1 fish that I put in a divided tank with another male and he absolutely SHREDDED his fins until I took him out about an hour later when I noticed. It all depends on the fish's personality whether or not they'll enjoy being in a divided tank.