"The areas of the body affected by frostbite feel cold and firm. Burning, tingling, stinging, or numbing sensations may be present" - from
MedicineNet"A block of dry ice has a surface temperature of -109.3 degrees Fahrenheit (-78.5 degrees C)." - from
HowStuffWorksTHIS chart gives various times for frostbite at different temperatures and wind speeds. In your case, wind speed = 0 because it's being held in your hand. Now, the table doesn't go as low as liquid carbon dioxide temperature. So I made a very rough plot. It should really be a hyperbolic function (so it doesn't cross certain intercepts), but this was the best fit Excel would give me.
Anyways, according to this VERY rough plot, a temperature of -109°F could give you frostbite in 0.214 minutes ~12 seconds.
I was bored, and did that out of curiosity. Long story short, don't do it again.