A place for more technical discussions. Please make sure you post in the correct section on the site, this way it keeps the site tidy AND ensures you get a more relevant answer.
When a cable becomes 'stiff' it's generally because the plastic coating on the inner wire of the cable has become 'rucked up' and is binding against the outer. This is a sign that the cable has been made cheaply.
For a proper solution, the cable outer, needs to have a plastic liner through which the inner can slide. Together they are self lubricating and not that affected by mud.
X-Eng has handbrake cables made by two companies. One of them (Elmill Products) will make pretty much any cable you like, usually cheaper than even a patterned part but so long as you specify plastic lined cable, the quality is very good. It generally helps if you send them the old one to copy. They are not fantastically quick - but worth the wait.