Sure, if you want to... but only if you're comfortable with the possibility of losing a hand if you mess up.
Here's what happens to a basketball when you freeze it in liquid nitrogen:
Maybe you've seen someone violently shatter a rose, a racquetball, or a banana in the same manner. What do you think would happen to your hand if you dipped it in a bucket of liquid nitrogen?
The answer is given by something called the Leidenfrost effect. Don't have liquid nitrogen in your house? Neither do I, and I'm a physicist who uses the stuff all the time. Luckily for you, the effect can be observed right in your own kitchen for no cost.
Put a sauce pan on your stove and turn it on. Once the pan starts to get hot, sprinkle some water on the surface. The drops should stick and quickly boil away. Leave the pan on the heat for several more minutes, then throw water on it again. If the drops of water dance and slide across the surface, you've just observed the Leidenfrost effect.
Chefs and home cooks alike already know this trick. If the water stays on the pan for a few moments, skimming across the surface, your pan is extremely hot, ready to go. Why, though, does a slower boil indicate a hotter pan -- shouldn't it be the other way around?
When a cool drop of liquid lands on a hot surface, heat is transferred to the drop from the surface. A large surface, with a temperature greater than the boiling point of the liquid, will quickly boil the droplet into a gas. However, when the surface is much, much hotter than the boiling point, something different happens.
An extremely hot surface transfers heat so quickly to the droplet that the bottom is instantly boiled. The boiled steam wants to rise, and so it pushes up on the underside of the droplet. The water is lifted up off the bottom of the pan, and floats on a cushion of steam. This tiny hovercraft can then scoot about on the pan surface. The steam beneath the droplet conducts heat up from the pan slowly; the droplet lives much longer before boiling away.
So here's the trick. Liquid nitrogen boils at -396 degrees Fahrenheit (-196 C). When you dip your hand (Briefly! Very briefly!) into liquid nitrogen, your hand is far far hotter than the chemical's boiling point. This causes the Leidenfrost effect to come to your rescue. The liquid nitrogen surrounding your hand boils instantly and is pushed away from your skin by the cushion of steam (nitrogen gas). This gives you an instant of protection before your hand is horribly burned.
Don't believe me? Here's a demonstration: