I have use outside air for my Equinox and am very happy with it. The reason an OAK is contentious has many causes:
1. Is it really needed? The test for this is whether the stove has draft problems unless a nearby window is opened a bit.
2. The outside location is important because you can actually create more negative pressure if the outside opening is located on a wall of the house that has negative pressure with prevailing winds
3. Long runs are to be avoided but some people on this forum have very long runs that work well
4. The outside terminus of the OAK is supposed to be at the same level as the appliance and not above it (by code) but once again, there are people running an OAK down to a basement stove that is successful
There a great Cdn. gov't information booklet that has some info on OAKs. The link is here:
http://publications.gc.ca/collections/collection_2009/schl-cmhc/NH15-436-2008E.pdf Since my OAK works fine, you can expect that I disagree with the info but it is a good general guide.
The relevant info is this:
It has been widely believed that smoke spillage could be reduced or eliminated by supplying outdoor combustion air through a duct, either directly to the appliance firebox or indirectly to the room in which the appliance is installed. However, research shows that outdoor air supplies do not work. When an exhaust fan is running, smoke spillage from an appliance can occur at the same pressure level, whether or not an outdoor air supply is installed. The same research shows that wind effects around the house can reverse the flow in these ducts, drawing air and possibly smoke through the duct to outdoors. This reverse flow can be hazardous if the duct is directly connected to the appliance firebox.A Guide to Residential Wood Heating 48 Canada Mortgage and Housing Corporation Some building codes still require that outdoor air be supplied to woodburning fireplaces. You must comply with this rule, but be aware that performance will not improve, and take steps to protect combustible materials around the duct from overheating if the gas flow reverses.
I think your idea is wrong to dump cold air and I don't think a cold air trap will work but maybe I don't understand (or misunderstand) your idea. However, there is nothing wrong in trying it, provided you don't create a reverse flue effect. Probably the great success of my OAK is just plain luck but it's 2' long and terminates on a south wall that should rarely have negative pressure due to house location and a bermed north wall. Of course, I get great draft with or without an OAK and that helps too even though my house was designed to be air tight. I actually have more of an overdraft problem with the OAK in place.