You need first to find out the source of the draft. It could be there is an opening in your chimney that brings cold air in from the outside. Some prefabs ae equipped with an outside air intake to feed the combustion. There may be a damper on that intake that can be closed. Aside from that, you should figure out a way to insulate the unit because unless you do that you will not be happy with any improvements you make. You might want to hire a chimney sweep to clean your unit and to ask him questions about it. -- just make sure the person you hire has some expertise on fireplaces.

If you have access to natural gas (or propane gas), you should seriously consider installing a direct vent gas insert. They are very energy efficient and safe, and will provide a serious source of heat. Unlike a conventional fireplace in which most of the heat goes out the chimney, with direct vent most of the heat radiates into the indoors, and the unit is sealed, so it does not affect indoor air quality. If you do a search of "direct vent" in this forum, you will find useful information about these systems.

If you have ice that means you have water. First, you must find that source and stop it.

I have always been a fan of wood. Gas can fluctuate in price and to me it's too much of a chance pricewize.
We had a zero clearance fireplace and we installed aa Avalon insert. We loved the warmth of the wood and the flame was very relaxing. They put a liner in our existing chimney and insulated it. We have power failures and I don't know how the DV unit works in one. But wood needs no power to operate.
We now use wood as our main heat source in our Vermont winters. Last year it cost under $400 to heat our home.

DV needs no electric power, although a blower will not work. But you get plenty of heat without the blower.

Wood fires are terrific, but when you get up there (I'm 73) it's nice to have a really good fire that's just a click away.

Ok, thanks for the info ... a few notes:

I don't have a water leak, the ice forming on the front of the unit is from condensation from the indoor air. The thin metal of the surround gets really cold... and the unit does have a external air intake with this cheesy lever for damper control; I think closed, it is actually closed all the way, but hard to tell.

I will check out the direct vent gas inserts; and power failure doesn't matter too much, I have a 6kw generator I converted to tri-fuel that I use to run the house when the power is out, which happens more often than I'd like especially because I am in the CITY (Ann Arbor MI.)

Thanks again!