The cables can be a problem... but it is just water inside the cable.
Where the inner cable comes out of the outer sheath, the sheath-end is terminated with a metal moulding with a rubber gaitor on the end of it. Unfortunately, the handbrake mechansim lever on the caliper, where the cable nipple locates, is higher than the lug on the caliper where the cable's metal moulding locates, so once water gets onto the inner cable it trickles down the cable, towards the metal moulding. The rubber gaitor is supposed to keep it from getting inside the cable.
The most common issue is the gaitor perishes and you get basically no sealing between the inner and outer cable.
The second problem is that as the handbrake cable flexes (on-off) the cable flexes between the outer sheath and the metal end moulding and eventually that bending-unbending movement causes the sheath to split round its circumference, so water can get in.
The inner cable is actually plastic coated so can't rust but the water can freeze.
Note if you leave the handbrake off and park in-gear, the cable can still freeze and then you won't be able to apply the handbrake!
It's marginally better for the cable to be frozen "off" I guess though, as you can at least try to pull the lever and see if that dislodges the stuck/frozen cable... whereas when it freezes "on" you can't really do anything about it.
If you loosen the cable at the handbrake and then diconnect the cable ends from the caliper handbrake pivots and pull them out of the caliper lugs, the cables hang down at 30 degrees and any water in there will drain out (if it's not frozen). Let it dry a bit (heat it with a paint gun or hairdryer) and then run some oil or aerosol grease or anything down the inner cable, working the cable in and out to get the gloop to go as far into the sheath as possible. Then ram some grease down the end or into the split.. that'll stop any more water getting in.
A pair of new cables is £30 from someone like Eurocarparts.