I have to worry more about Texas heat hurting my rabbits, than the cold getting them. I have a three tiered pen so they have the top tier for sleeping, the middle tier for food and water (there's a barrier between these two tiers so poop doesn't fall in the food/water), and the bottom level sits directly on the ground. The entire thing is moved to a different area of the yard once ever three to five days. The cage is hosed every day.
The rabbits seem to have adapted to the weather and temp changes. Like you, I was concerned when it started getting cold at night. We tarped once or twice but now they just stay out there no matter what -- except that I take extra precautions if there are heavy rain or bad storms.
My rabbits are fed one cup of food each, and they are fed every morning. They nibble a lot during the day and there will still be food in their bowls when I go to bed at night. By morning, that's all gone.
They are also fed alfalfa, other green stuff, and leftover cereal from breakfast. Their favorite is that chocolate cereal with marshmallow things in it.
In the summer, about once a week they got to swim in a wading pool which they really enjoyed.
The rabbits are kept where the birds can't roost on their cages.
I collected a lot of political signs after the elections and secure them to cages when I'm concerned about temp, weather or wind. The signs are weather proof and easy to put on the cages and remove after all is well again. They do look funky, however, and I'm not real sure how the politicians would react if they saw their signs on my hutches.
Once when it was going to be cold at night, I rolled up an old sheet and put it in the hutch thinking they'd tunnel into it. What they did was chew holes all in the sheet. I won't be doing that again.
Best of luck with your rabbits! We just love ours!