You can tow any trailer without a brake controller, but it wouldn't be smart with a heavy trailer. I don't know if it depends on the state, but here it's against the law not to have brakes on a trailer over 2000 lbs.
If you have the 7-pin trailer connector on the back of the truck, adding a brake controller is super simple for aftermarket and pretty easy for OEM factory controllers.
For after market controllers like the very popular prodigy controllers, you just mount it under the dash and plug it in with a RAM adapter cable and your done. That's it, no splicing at all. Prodigy is the most highly recommended controllers over on the RV sites.
For the OEM controller, you also just plug it in, but you have to have the dealer flash the computer for a price and have to take part of the dash apart to mount it where it goes.
Ray