The Arduino Uno documentation I've found states that a 12V DC wall adapter can power an Arduino using the barrel jack or USB inputs, and that the vin pin can be used to power the board using a 9V battery. I'm wondering would it work if I tried to power the board with a 12V DC wall adapter via the vin pin specifically? My high-powered LED running via a PicoBuck needs somewhere in the neighborhood of 7-12V to run, I want to also power the Arduino board off the same wall adapter, but need to know if my vin pin plan will fry my Arduino.
You can power your Arduino with 12V to Vin, but it's not recommended. There is a regulator on the board with a tiny heat sink. The regulator is prone to getting too hot, which makes it shut down to protect itself. Ideally feed 5V into the 5V pin. If you don't connect much to any of the output pins of the Arduino then 12V will probably be okay, but be aware of the potential problems.
My own rule of thumb is if it's too hot to keep your finger on then it's too hot.
Temperature of voltage regulator depends from input voltage and current. Arduino UNO itself doesn't consume too much. And since you have no additional loads like bunch of LED connected to arduino pins you should be OK with 12V supply.
The voltage regulator heats up due to power dissipated. Power dissipated is the voltage dropped (12 - 5 = 7 volts) times the current drawn, which, to limit the power dissipation to 1W as discussed above, means a maximum current draw from the regulator of 143 mA (7volts x 0.143 Amps = 1.001 watt).
If the UNO and all its connected devices draws more than 143mA, then the reg will heat up and may fail. Do you know what current is drawn by the UNO and attached peripherals? If it is lower than 143 mA then all will likely be okay. Just as PerryBebbington says above, I wouldn't recommend that approach, but it should work. Preferably provide 9volts to the barrel jack or vin and you could then draw 571 mA.
Average current for Arduino Uno itself is less than 50mA. And LED modules powered directly by 12V power supply, so your are safe even with 1W regulator power dissipation. But this 1Watt dissipation is for minimal pad. A Uno usually has an extended copper pad under a regulator so it can dissipate noticeably more than a Watt.
