Re: Would a cold air intake..........
I have my own cold air intake, it sucks out of the passenger fender. I have no heat riser off the headers.
If you cut out that plastic thing that is on the opposite side of the core support (it twists out by the way so you don't need to cut it) then you'll have dirt, bugs, water, and snow going up into the plumbing. I have experience on this matter.
In the wintertime I remove my tube that goes between the air cleaner and the fender so it sucks in engine heat.
For each 5°F decrease in air temperature you gain 1% horsepower (rough equation based on air density). That means if it's 70° outside and 150° under the hood you can gain 15% more ponies by sucking air from outside rather than an open element as long as you aren't sucking from a low pressure zone or have restriction.
150° is a reasonable temperature for underhood since that's right about when gasoline starts to boil.