I have a similar problem only X2, plus made infinitely worse because of the minus 40 degree celcius weather up here in Canada. My problem is so bad, it shuts down my furnace every morning when the main furnace starts to heat the house back to room temperature (I run the thermostat at 18C at night).
My home has 2 high efficiency furnaces - the main furnace for the basement and main floor, and a smaller unit for the upstairs. On the north side of the house, I have two exhaust vents roughly a foot apart, and two intake vents, one on each side of the double exhaust vents. The exhaust vents both develop ice all the way to the ground. The main furnace intake (the one to the west of the two exhaust vents) will go from completely clear to completely plugged in 30 minutes of furnace operation in this weather.
These are the worst conditions I've found anywhere in discussions on the 'net. Worse yet, none of the solutions offered by fellow sufferers or by HVAC professionals will work for me. However, I have devised a solution that works, and it's cheap and simple. I placed a piece of plywood (2' X 3') between the exhaust vents and the intake vents on both sides. I didn't need to affix or attach them in any way because there happens to be enough snow on the ground, but you might need sand bags or loose dirt piled up around the bottom on each side of both sheets. I angled them from the outside of the exhaust against the wall over to the inside of the intake out at the end away from the wall. You get a bit of a V-shaped enclosure with both exhausts inside the "V" and the intakes on the outside of the "V" on both sides.
Incredibly, this works under the worst conditions because it channels pretty much all of the moist exhaust air away from the intakes. Even the shortest possible distance from the exhaust to the nearest intake is made 4 times longer with this approach. This is far enough away that the moisture is sucked out of the exhaust air before it gets to the intake opening. The problem has disappeared completely since I stuck those "baffles" in there.
Best Answer
As you just noted gas exhaust flues get "pretty hot". Which is the reason they should not be in contact with combustible material. Also they need to be 'double walled' if they are passing through an enclosed surface. Also be sure the vents terminate to the outside, but not in close proximity to any windows or return air registers.