Outdoor housing can be great if you take care to do it properly and are committed to really spending a lot of time out there.
Securing the dog run is a must. Instead of chicken wire, you might try hardware cloth (what I use on my chicken coop). It comes in 1/4 - 1/2 grids and is much stronger than chicken wire (hands down). It'll keep your rabbit in and reaching raccoon hands out) if you wrap a 24 inch strip around the outside bottom of the run and secure it. Do the same with the top of the run. You don't want it open. Opossum and raccoon are in every suburban and urban area. Just because you don't see them does not mean they're not there. Making a cover of chicken wire will be fine for the top. It will be enough to deter a persistent raccoon trying to find a way in. Just make sure to not leave holes that it can squeeze in through. I've usedmetal "C" rings to make chicken wire "blankets" for chicken run roofs. It's good that you have a cement floor.
Besides completely securing the run top, bottom and all around, you'll need to consider the basics - sun, draft, damp, heat, cold, ventilation, and sanitation.
What's your plan for the cold winters and hot summers?
Stuffing the hutch with the hay that your rabbit normally eats works as an excellent, edible insulation for your rabbit. It will make it's own burrow and hang out in there when it want privacy, warmth, and a dry place. You'll be suprised how well rabbit do in the cold and you'll probably see your rabbit out enjoying it more than one might think.
Rabbits can begin to stress when temperatures get to 85 degrees so you need to have a plan for cooling your rabbit. I prefer cooling the air around the rabbit as opposed to wetting ears or leaving frozen water bottles for it to lean again.One good way to cool the air aroundyour outdoor run is to string up a line of fine misters connected to awater hose. Don't place them so close to the rabbits play area that it soaks the rabbit. That is not the goal. You wantto mist the air. The mist will cool the air around the enclosure. Any breezes - evenwarm breezes will feel up to 20 degrees cooler inthe run (under the tree).
You'll also want to keep an outdoor thermometer in the run so you can keep tabs on the temps. I've used a remote thermometer from Target that allows me to know what the temp is from inside my house. Some of those types can be set to have an alarm go off once a certain temp is reached. Still, in summer, I visit weather.com daily to get weather predition highs for the following days to I can be plan accordingly to make sure I'm home to monitor the rabbits during the hottest parts of the day and do what I need to to keep them comfortable.
The tree should protect from the sun. I rabbit can do well under a tree but direct sun (heat) could kill it on a warm day. Give it protection from rain or damp. Keep its bedding clean and dry.
If you choose to close up your rabbits' enclosure, make sure there is very good ventilation.
What is your plan for sanitation? No matter the size of the enclosure, a rabbit have a clean environment to be in the best of health. It helps me to designate specific cleaning days.Cleaning twice a week is okay in this type of enclosure. Fyi, the fly reproductive cycle is every 5 days so cleaning twice a week like clock work will disrupt it. Still, there will be flies (there are always flies outdoors) so putting up a scent bait fly trap once a month or as often as neededwill help. Adding food grade DE to pelleted food (use very, very, little) will not only naturally deworm your rabbit of some parasites but kill any fly larva that hatch from eggseither in the rabbits run or the compost pile because it will be in your rabbit's droppings.
This might all sound like a lot to consider and do but once you get your "system" set up and goind, it can work out very well for both your and your rabbit. Just make sure that the area that you set up for your rabbit is one that you want to be in, too, because you're going to be spending a lot of time out there. If you realize, once you've set it up, that you don't enjoy being out there, make changes so that you do enjoy being there to spend time with your rabbit or explore ways that you can keep him inside safely (a whole 'nother ball game that can be very fun once you know how to do it).