We have a gas fireplace in our family room. It's an insert in a masonry
fireplace, and is not direct vented (but vents out the chimmney).

It's cold. On a cold day you can feel cold air coming in through the
front of the fireplace where the combustion air is supposed to enter.
At first I thought the air was from around the fireplace itself, and
stuffed insulation up the chimmney (not blocking the flue, it's a pipe
all the way to the top of the chimmney) and around the masonry firebox,
which helped quite a bit but there's still a draft coming down the gas
fireplace flue and into the house. I have not been able to figure out
where the air is going.

Another problem this causes is that the firebox is very cold. When it
is, if you try and light the fireplace (it has a pilot) water vapor
condenses on the logs and extinguishes the flame, causing a strong gas
smell. You can literally see drops of water on the glass on the front
of the fireplace. You can only get the fireplace to light correctly if
it's warm, so I have taken to using an electric space heater to "prime"
the fireplace so it's warm enough to prevent the condensation. Once the
fireplace is started it works fine until it cools down after being off
for several hours. If it's not too cold the heat from the pilot can
keep the firebox hot enough to prevent the condensation as well. When
the firebox is hot there's also no cold air coming down the chimmney,
obviously.

We had the fireplace checked out last year and I was told the cold air
coming in was normal since the flue has to be open. I can't imagine it
is if it makes the fireplace unable to ignite safely. I would also
expect warm air to rise, and go out instead of come in. We do have
another fireplace in the living room, which was woodburning and has gas
logs (not an insert) in it. The fireplaces are about 20 feet apart.

Any thoughts?