unwanted visitors

I've only had my buns a few weeks and they are outdoors bunnies (although I always intended them to be outside, I've tried them inside several times just to see what they were like and they HATE the wood floors, it makes them very grumpy and thumpy).
Anyway, i am wondering how to tackle the problem of rats and mice in winter? will they actually go into the hutch when the buns are there? what are the other dangers?
My 2 get fed 'downstairs' at night with their hay upstairs. The hutch is about 6 inches off the ground but I know this won't deter hungry rodents. It has a hutch cosy cover and will also be covered over with carpet etc at night when its cold but I want to make sure they are as safe as possible. A neighbour diagonally across from us keeps his 2 dogs outside and we have had rats in the past.
Hopefully by the winter we will have moved house and they will be in a shed but I'm starting to worry already.

As long as you only give them as many pellets as they can eat in 5-10 minutes there will never be any food laying around and in turn you shouldn't attract rodents.

thanks for that, they get their greens at night just now rather than their pellets, which obviously is quite a big bowlful between the 2 of them, and they don't eat them all in one go, they 'graze' during the night. That's why I was thinking I should worry about other furries. I think I will have to swap their food around when it starts getting colder.