You might be able to mimic cold temperatures somehow but the varieties you want to grow (in Florida, I presume)may not take the heat that we have during the summer months.

When you live in FL it isn't easy to grow things that are grown up north. Adapting is the less stressful choice. We are limited by salt intrusion near the coasts. Then, it is colder inland FL than it is on the coasts in the winter but it is dern hard to find a hard frost except in north FL or up in the Panhandle. We move to FL to avoid such atrocities!

I have a good friend who lives in Dixie County about an hour west of Gainesville. Her place can get down into the teens in the winter, but not for long.

Asparagus didn't even work for me when I lived in the Atlanta area. Nor did rhubarb.

You might be better off looking into Tennessee or the Georgia Mountains. You are asking to change a lot of the good reasons we come to Florida in order to conform to your requirements.

Addressing a few questions from your post:

"So, I'm wondering if it's possible to create conditions that mimic 'overwintering'. That is cold temperatures."

Not that I know of, short of buying a fridge big enough to hold whatever you want to overwinter. There's nothing wrong with experimenting with non-adapted plants occasionally. But you should mostly grow plants that like it here. If you try to recreate your zone 5 garden in Florida, you may harvest a lot of disappointment.

"I'd like to attempt to do this, because there are many varieties of fruit trees and berries that require this. Fruit trees require a certain amount of hours with chill hours to set blossoms, fruit, and sweeten the fruit."

You are correct about the importance of chilling hours. For this reason, there are a LOT of fruit-breeding programs which breed low-chill fruit varieties. There are Florida-adapted varieties of apples, pears, peaches, plums, nectarines, strawberries, blackberries and blueberries, which will grow in all but the most southern portions of the state. Grapes and figs are naturally low-chill, but you will need varieties that can handle our humidity and disease pressure. There are also a lot of interesting subtropical fruits you can grow in most of the state, and if you live far enough south you can even grow tropical fruits. So although you won't be able to grow, for example, a Golden Delicious apple, you will be able to grow a Dorsett Golden apple, as well as many other fruits and berries.

"Last but not least certain varieties of vegetables just taste better after a hard frost (this is regarding established plants, not seedlings/young plants). First things that come to mind are collards, kale, and parsnips."

The nice thing about Florida is that we can get food from the garden year-round. There is a wide variety of vegetables that can be grown all winter - including garlic (plant in fall, harvest in spring), collards and other greens, carrots, lettuces, radishes, and much more. Central Florida and northward get frosts every winter - enough to sweeten your collards and kale. I'm not sure what the S. Florida folks do to sweeten up their greens, but they get home-grown tomatoes in the winter, so life down there has its compensations!

Here is a link that might be useful: Florida Vegetable Gardening Guide