Would you want to sleep in winter, in an uninsulated house, and have a run that rain and snow could dump on your head and cold wind chill your bones? Neither would your rabbit.
Very importantly, bunnies should have plenty of space to run and play year round. Keeping them shut in a hutch because the weather is bad is not the way they should live. A good sized secure (fox and escape proof) run attached to their house or with their house inside of it or attached to it, is imperative to their quality of life.
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Recommended supplies for winterising:
straw/hay - When it turns very cold (December-Feb) pack at least 6 inches deep in the room they sleep in, and change it and clean the floor every week if they pee in the house (ours are litter box trained, even the outside bunnies); you can go two weeks or so longer if they are tidy bunnies - but be sure to top it off regularly to keep it well stocked for warmth. Straw has great insulating properties and makes a nice soft bed.
bubble wrap - staple to the top of their house (if they can not get on top of it) or underneath (if the house is high up enough they can not chew it from below); also on the houses that are outside the runs, such as Vuvu and Max's converted chicken run with upper level house, I have it also stapled inside onto the ceiling of the house (the ceiling is over 1 and 1/2 feet).
wool flannel - you can use blankets, in the UK you can find them at Edinburgh Woollen Mill shops, and I buy mine in spring and summer when they go on sale. Staple them to the walls or ceilings. Bunnies tend to not chew real wool or knitted acrylic. Wool is a great insulator. Cut to fit.
clear plastic sheeting - Get the good thick stuff and staple to the outside of windows on their houses and also the walls and doors of their runs. On the runs, leave around two inches around the top on their other sides if possible. Shower curtains make great thick sheeting! Even better:
clear plastic perspex - screw (so you can remove in spring) to the sides of runs. I keep this on the roofs also all year round for rain proofing. Again, leaving a few inches at the top for ventilation. You do not have to cover the entire sides top to bottom either; if you get from the top to a meter down, you will keep out most of the wind and rain/snow, as well as, you will want it to get some air circulation or it will get damp inside (I leave a few inches at the bottom; if it has wood covering the sides at the bottom, the wood will breathe). When we use it on the tops, we have also crossbeams of wood to support it, or it will bow down and even break with the weight of a heavy snow. Remove snow if it is more than a couple of inches deep from it as soon as possible to keep it from building up and bending the roof. I use a broom, it's easiest.
above, carpet tiles for floor insulation; plastic sheeting and perspex on walls of the runs for rain, snow, and wind protection
above, fake fur (a recycled coat) stapled securely to the roof for insulation; and carpet tiles and soft bedding for warmth (if they decide to chew the carpet tiles you will need to remove them)
insulate - staple or nail or screw on wool blankets, duvets, or sheets of felted wool inside their houses to the roof and walls - make sure they can't reach the duvets if they are chewers
ventilation - make sure there is a source of fresh air, this is important; it should not be a large opening (which will let lots of cold air in) but you do not want them sealed in with no fresh air; if the run connects to a house, then that provides ventilation if the run has ventilation
below left: duvet and blankets stapled onto ceiling and walls in a shed; right, plastic perspex on the outside walls of a run attached with screws
soft bedding and carpet tiles - I use these in their houses for warmth. It's nice. The carpet tiles are inexpensive and can be chucked if they become grubby. They're also easy to clean with some water and a brush and a bit of sunshine to dry in. Soft bedding, I use the Ugli Donut bunny beds (www.thehareapparent.com) that I make as well as wool jumpers (remove any buttons, zips, or tags) make a nice soft bed. Plenty of hay and straw (mind they will probably poo on it so replace it weekly).
heat - Hot water bottles wrapped in fake fur or thick knitted wool keep their heat for many hours. Also I use the Snugglesafe heat pod which you microwave. It's pet safe. I put it in their houses at night under their beds and on top of the carpets, sometimes with a soft rug on top too to keep the heat in. Best price for those I have found is Amazon. Avoid fake ones sold for cheap on Ebay.