I just put a new 350 in my car with a performer intake, 600 cfm
performer carb., TES headers and 3" exhaust. My problem is that
in the early fall when it was warmer out (70's) the car was running
great. It had a small hesitation off of the line and if the gas was
punched, but it was bearable. However, I just went for a ride
this afternoon and when I punched the gas from a stop it
would just bog, sputter, then take off. The temperature outside
today was in the 20's, so I am just wondering if the cold air is not
allowing the fuel to atomize properly and if this could be causing
the bog?

 

It's pretty likely that the original hesitation was caused by an insufficient pump shot..making it go momentarily lean.

A cold carb will run leaner than a warm one...it'll make the original problem more noticable. Of course..it's also possible some other problem popped up, so so a check for vacuum leaks, proper pump operation, etc.