This only happens with cold weather, usually around 40 degrees or colder. It gets worse the colder it gets. In this video it is 22 degrees outside, but currently feels like 10 with the wind chill.

Basically what happens is what is shown in the video. You turn the car on and within about 10-15 seconds it starts making that clicking noise. It sounds like it's coming from the fender region, not necessarily sure where. It will bog down and rev back up like it does in the video, sometimes shutting the car off once or more. Usually after about 20 minutes or more depending on how cold it is it will warm up and drive fine.

Not exactly sure what the problem is.

The car is a 1996 Honda Civic LX 4 Door with around 75,000 miles on it. It's taken care of and well maintained. The car was always in a garage till about 5 years ago where it is now always outside.