Welcome to the Forum!
It’s best with hog houses to only put a handful of material in to start with and make sure there are lots more material nearby for the hogs to collect for themselves. That way the hogs can choose their own material. They are far better at building nests – especially hibernation nests – than we are. Also, most hogs prefer to do their own interior decorations. But that would mean it would be up to the hogs whether they mind ivy or not. I would be inclined not to include any ivy in the handful you put in as the starter. In general medium sized leaves, long grasses, etc. are best.
Good luck. I hope you get a tenant soon.