If you're not worried about the look of the cable running up there, fine, some people aren't. My wife would have a fit if I did this though.

Also, since most cable comes into the house before being split you'll have to drill 2 holes....one to get it back out after you split it, and another once you run it up the wall of the outside of the house to get it in through the closet.

You will need a "Hammer/Masonry(assuming your house is brick) Drill with at least an 18" long and 1" thick bit. Expect a lot of dust as you'll be going through about 12" of concrete.