I came up with something and I feel like I should post it for what it's worth.
We live in New Hampshire and over the past few months rats have moved in. We have a rabbit hutch and 6 hens in their coop. The rabbits dug a tunnel network and the rats moved in. Then the rats dug their own network under the chicken coop. We had countless (10+) rats running around every night in each place.
I tried traps and they did nothing. The rats are too smart. My wife won't let me use poison or shoot or burn. So I had an idea.
We had a real hard cold snap for 4 days. Once the ground was super frozen I filled up 2 5 gallon buckets with water and put them outside on the porch. Every 20 minutes I would go break the top ice and stir them to get the water the very closest I could to freezing. When the ice crystals were forming throughout the water column in the buckets I dumped them on the rat tunnels at the tunnel's highest point.
Apparently the combination of almost-freezing water, frozen ground and gravity was pretty lethal. We have only seen one rat since then.
If anyone wants to duplicate the experiment I'd like to know the results. I hate the idea of using poison and killing predators. We had a very well fed owl that helped with the problem but it could only eat so many rats.
Apparently for us a frozen flood took them out. Hope it works for others. Its a solution available to those of us who still get winter.