I have read that many people use a water displacement lubricant such as WD-40 to prevent the freezing. They did suggest spraying enough product in the cable housing to flush the water out if you already have the freezing problem. That seems to be you.
WD-40 is a water displacement product, hence the WD in the name, 40th formulation.
I personally don't care for it as a lubricant, but I think I recently read that they had made some changes to the formula to improve the lubrication.
Here's my suggestion; Prestone de-icer. It is bragged to last for quite a while. Some people spray thier vehicle windshields with it in the evening and supposedly it keeps ice from freezing on the windshield till morning. I did't try that yet, but it works good in keeping ice from freezing to snowplows and shovels, so I suppose it's worth a try on your chute cables.
Went ahead and ordered new cables, and am going to use Tri-Flow Superior Lubricant - Will saturate the cables as much as possible, and
hang them in the house for 3 or 4 days before installing them - Local bike
shop uses Tri-Flow a lot for cables, chains etc. on bicycles - hope this will
Snow blower shop says the moisture occurs from cables heating up and cooling down, and moisture condensing in the cables - hopefully I can displace the moisture with the lube...
Tri flow good stuff on the expensive side though but lasts just about forever. I got a little throttle cable freezing myself mostly when i like to cut the banks and throw to that side. Usually move the throttle after each pass keeps it free. Its a hassle might have to move it a bit more often to keep it free