Why did the troops perform so well in such horrible weather at Trenton in December, 1776?
They were highly motivated.
The weather really was not a factor though. It had snowed and was a bit blustery but nothing unusual for a December day. The true success of the attack was that it surprised the Hessian troops. They were unprepared, sleeping and hung over.
If you had asked Washington just prior to the attack, you would have found him skeptical of success because he had place a very high premium on catching the Hessian troops asleep before sunrise. As it was, the attack was late and happened after sunrise.