I've raised Fallow deer before. Easy keepers. Stayed in a 4' fence for years, then learned to jump. At that time they were considered farm livestock, no gov. requirements. Laws have changed, now require a 10' fence, inspections, etc. Same laws for whitetails.
NO not really. First of all in almost every state deer are strictly regulated because they can carry some of the same diseases as cattle. And as a "wildlife" hunting species, in general you would be required to have a permit in order to confine the deer in the first place.
In order to acquire the deer in the first place, you have to buy them from an approved dealer, you have to have a permit and appropriate fencing. Appropriate fencing is either one 8 foot fence surrounded closely by a second 6 Ft fence or an even higher since fence to prevent escapes.
Finally you have to have the deer tested for TB, and CWD, and a few other diseases. Depending on the state you live in, you have to have "permission" to "import" them from a different state. and basically jump through ton's of hoops to finally get a few to your place at some great expense.
And lastly, you DO NOT want to attempt to hand tame any bucks. Bucks that are handled as young and hand tamed are downright dangerous in most cases. Doe's on the other hand are very nice as hand raised animals.
No it is not possible to ride a deer ( if you mean either white tail or mule deer) because neither is really big enough or well suited temperment wise for riding. I've however seen both Moose and caribou put under harness and used to pull a cart or wagon. But again you have to raise them from babies, have the appropriate knowledge and skills to deal with their flight instincts and you have to have the appropriate permits to keep the animals or face time in jail.
Why are bucks that are handled and raised young dangerous in most cases?
No, it is not possible to ride a deer. They are all rather frail and fragile. I think their legs would collapse and they would freak out if you hopped up on one and tried to ride it down to the local super market.
Deer are weird animals. I lived in the hill country of Texas and deer roam around freely in yards. In some of the lower populated neighborhoods, the deer will come right up to you and eat out of your hand. Most of them though won't let you get anywhere near them. They take off running once they notice you are walking towards them.
Commercially raised European Red Deer might be the exception for ease of raising domestically, with the proper fencing and permits of course. If you're absolutely resolved to ride a wild critter, may I suggest a hand raised Grizzly bear, bison or maybe wild hog? Deer aint made for riding without the third E on the end of course