Our Goodman furnace (installed Oct. 2007) runs fine until it reaches 10 below zero or so. Then, the grid cover on the inlet pipe, which is next to the venting pipe, becomes frosted over which causes the furnace to stop running. We have had to go out several times this winter at all hours, and in the most frigid weather, to take off the pipe piece, scoop the frost out and reconnect it. We have awakened one too many times to temps in the 50's in our house. What a poor design!

Those are typically put on to keep wasps and other insects out. Get a small piece of hardware cloth and make a screen.

I ran into this very same problem a number of years ago. My solution was to get the intake & exhaust far enough apart to prevent the exhaust from going into the intake.
A concentric vent kit works very well to cure this problem but it takes some work & repiping. They are best installed from the start.
My guess, in your case, the problem is installation, not furnace design.

Mine were turned about 90 degrees apart. Never had icing but sure had mud daubers.

If both pipes have elbows, particularly if they are pointed down, it will certainly cause a problem. If you have enough room, cut the exhaust pipe at the end of the elbow so it blows straight out. You can put on a coupling and a foot or two of pipe (don't glue it at this time). This "patch" should get you through until a proper fix can be effected.