302 won't stay running

I need your guys help! I've got a 66 coupe with a 302 in it that won't stay running. It had sat for a day due to a big snow storm and when I went to start it, nothing. It took a while and drained the battery but I thought it was normal because it was cold and had happened before. When I finally did get it started it ran perfectly normal for about a minute then shut off on its own. I restarted it but the idle was now so low that I had to bump it up on the carburetor to keep it running but it would still shut off randomly. I got it to run long enough to get to the store but on the return trip it would sputter and backfire at any speed and eventually shut off all together. it was towed back to the house and I have replaced the points (which were bad) and the fuel filter (also bad). But it is still doing the same thing. The dwell is dead on and I recently set the timing but it was running great before that storm.
Any Idea what is going on.

Thanks for the suggestions guys but it turns out that it was the condenser that was craping out on me. I'm just glad that it was something small and inexpensive and not something big.