Your heat problems are probably due to your wearing the wrong kind of socks. If you're using cotton socks then switch to nylon socks so that the moisture and heat won't get trapped. If your running socks are nylon then go to a thinner pair.
Some shoes breathe a bit more than others but the only difference I find between my Shimano SPD MTB shoes and my SPD road shoes are in the stiffness of the sole and the lack of walkability. I prefer the harder, stiffer sole of the road shoes on my road bike simply because that's what I've always used on road bikes since I get cramping issues in my feet with a softer more compliant sole.
As for the cold weather, I've got a pair of Garneau neoprene booties that fit over either pair of my shoes. They keep the water and wind out. I'll still use nylon socks regardless of the weather. As a matter of fact I'll use the same kind of socks for x-country skiing. If it's really cold, then I'll use merino wool socks which could be another option. Both nylon and merino wool are water wicking and will keep your feet happy in cold or warm weather.
As for going sockless ? Dunno about that. Aside from the fact that my shoes would probably smell really bad, I'd probably develop blisters at some point..