I feel bad for a wild rabbit who's living under my deck in the snow & below 0 temperatures. Is there anything I can do?

I don't really know if I can do anything for the little guy, but I feel so bad for him. It's windy and there's at least 4 feet of snow on the ground.

I was making myself some dinner a half an hour ago and I saw him outside my kitchen window (which is next to the deck) sniffing around in the snow near the deck. It's an elevated deck, so we store some old bins and our tractor under there. My mom says he probably made a den under the tractor for himself.

I want to help him, though, so I stood up on the deck and threw down an ear of lettuce. It's probably bigger than him, lol. I also threw down a carrot or two, but carrots are pretty sugary.

I have my own rabbit so I have hay in my house. Do you think I should pile some of that down there for the little rabbit? I don't want to completely intrude his space under my deck, but I feel like I should at least give him some food.

I wanted to make one of those box houses people make for feral cats, although I don't think my mom would let me and it'd also require me going under the deck to position it and I don't want to accidentally chase the little guy out.

Should I even be feeding him? At night, he searches around my yard for food. I see his paw prints on my front porch and in the paths my dad snow blowed out for my dogs in the yard. I just feel bad. He's probably freezing and starving.