Assuming you have a standard frig -- as opposed to the small/short ones found in college dorms:

1) might get too much heat from the frig

2) insufficient light would be a big issue

3) how big a terr are you considering?

4) would you actually get to see it at all?

These are issues I was thinking about. I was thinking about putting a timer controlled growlight on top as well as 120mm computer case fan running at low speed to ventilate somewhat. The view is what got me the most. The only other viable place is on top of my dresser, but I'm not sure if I want a terrarium in my bedroom.

Maybe a floor plan might be helpful.
By small apt I take it that you mean a studio apt where the only real separate room is the can.
Just where are your windows located and can they be opened?
What is the orientation of the apt: windows on east, west, north, south? Door on E, W, N. or S?
If you are going to grow carnivorous plants then you would not really need a full terrarium set up and could have the top of the terrarium opened for some time during the day as long as the plants have some humidity and the amount would be dependent upon what carnivorous plants you were planning on using. Light is the real need for these plants.
Another consideration is how warm do you keep the apt?
Also what about the bathroom? Any ledge space in there?

I don't see anything wrong with a terr. in a bedroom. I have one (10-gal) on top of my dresser; I have an 18" under-cabinet light on top with a timer turning it on from 8 am to 8 pm. I also have another 10-gal right next to it on a stand. Both lights run through the one timer.
-Jmcat

It isn't a studio apt, and the window in the BR faces W, in the LR, to the E. It isn't feasable in the LR, because the window is raised and I already have a chair underneath it, having no where else to put it. And in the BR, the window is 5 feet from a privacy fence and the view is of weeds and garbage (there's no gate access). However, I am getting a bookshelf for the BR soon, so I might consider that as an option. All I need to know now is being winter, how much light would flytraps and pitchers need? Oh, and the humidity here in Lubbock is always really low, so I'm not sure if keeping it open all the time is a good idea or not.

Below are all the links that I have in my Favorites on carnivorous plants sites.
Pitcher plants can handle direct sun while flytraps can handle direct sun as well though the time of exposure required is less for them. Check the links below for more detailed info on their culture and I do believe indoor culture is covered as well. I grow mine outside (coastal California).
Lubbock! If I am not mistaken, there is a rare Sarrencia species that occurs in your part of the state. The humidity here can vary from less than 30% to saturated whenever it rains but generally 30%-50% seems about normal. I supplement by misting the plants once or twice a day or more as I feel it is needed. I grow Sarrencia purpurea and Sarrencia psittacina, Darlingtonia california, and Heliamphora minor outside with the H. minor in full sun for most of the day but on a drip system to keep water moving through the substrate.
RECOMMENDATION; learn how to grow the plants and then figure out how to adapt your spot for them. Got space for a Hex tank????

>CARNIVOROUS PLANTS
http://www.californiacarnivores.com/
http://www.carnivorousplantnursery.com/
http://www.cascadecarnivores.com/
http://www.cobraplant.com/
http://www.cpjungle.com/
http://equilibriocarnivorousplants.com/
http://www.flytraps.com/
http://www.mycarnivore.com/
http://www.petflytrap.com/
http://www.tristanscps.com/DesktopDefault.aspx
http://www.sarracenia.com/faq/faq6280.html
http://www.utricularia.net/englisch/index.htm
http://www.omnisterra.com/botany/cp/pictures/drosera/0075.htm#D.acaulis
www.wistuba.com