I run a 351W in my jet boat and it is tempermental in cold weather as well. In fact I had to use a bit of ether the other weekend since the choke was not seeming to work. My engine will start up when it's cold and die out after a couple of seconds because it is not choked properly (could be your issue). It will however start up again and run for longer periods of time until after the second or third try when it just starts running normal. If you are getting ethanol free then I do not see how it could be a gas issue. I gave up on that hassle a long time ago. I just get premium gas and add in the marine sta-bil every tank. Sta-bil takes the water out and controls the problems that ethanol creates. I know a lot of people who still run ethanol free only but I have to say that it is not worth the extra effort to go so far out of my way for something a 4$ chemical can do.
For all outboard questions, see dealer
They are complicated heads that I wouldn't touch with a ten foot pole.