If you have to leave the handbrake on, and it does seize up then it is most often caused by corrosion of the working surface of the disk/drum "welding" onto the pads/shoes. This can often (but not always) be released by releasing the handbrake and hitting a wheel nut on the effected wheel with a hammer HARD. With steel wheels this is easy, but with alloys the nuts are often recessed, and in this case put a socket (of the right size) from a tool set onto the nut first, and hit the socket.
Normally 2 or three blows are enough.
Of course the cables can seize, as can other parts of the system.
It is also not unheard of for the cables to become full of water, and freeze up in cold weather- in that case all you can do is fit new cables or wait for the weather to warm up.