Having trouble starting in cold or wet weather

I have been having trouble starting my car when it gets cold, or is wet out. About a month ago before these problems started was heading home when it was raining felt my car bog down like I hit a deep rain puddle, got out nothing was broken or leaking thought everything was fine. But since then I have noticed that when it gets cold or raining out that it has trouble starting the engine turns, and will sputter but not start. Also I have noticed that the longer I turn the key I get a lot of gas smell like its running rich. And a bit of smoke