Kevin,
Stan has about nailed it. If you are thinking Speedster, I can only guess your weather is going to put you in a bad frame of mind more often that not. If you are thinking of 356-style and have some serious affection for the badge, as it were, and can give up on the ragtop, how about a Coupe? JPS (North Hollywood, CA) is developing and now selling an A Coupe replica that will promise weathertightness (?), and much else in creature comforts. JPS is a quality builder, currently assembling a Speedster for me. The compromise, I guess, would be the convertible D, which is made w/ roll-up windows and other things I am not aware of. It's not a Speedster, exactly, but the top will go down. I suppose they are weather-tight, but have no first-hand knowledge, being a bit new to the replicar game myself. Others here in this Forum will have much more to say, no doubt. I can tell you that I once owned two 356 Coupes, and used them as daily drivers, in all sorts of weather, for a combined about 15 years ('60s and '70s). These original cars were never much for heat in the dead of winter, and truth be told the poor rubber used allowed water entrance around the rear window over time, but still these cars were my daily ride. I would have them still except for the dreaded cancer: rust. Living in foul winter weather on the US east coast brought these otherwise wonderful cars to their knees. I did not have the resources required to restore them. The replicars you might consider in the current epoch will not have this problem.