You don't mention the exact Electra that you own, but suffice it to say, you have a very relaxed geometry bike there. Bikes like these are hard to generate a lot of power on, which could be problematic. I also have no evidence proving that they are "better" on ice.
I run a rigid hardtail in both snow and ice and get along well in both conditions with a few exceptions. First of all it is important to keep the big picture in mind. A bicycle isn't the best vehicle for riding in the snow or ice for that matter. Sure a lot of us here are doing it but it's because we love riding and this is just another form of that, albeit not the best sometimes.
In reading a lot of posts, sometimes it seems like there is the notion that there is the perfect bike out there for riding in snow. Maybe some are better than others but all in all, a pair of snow shoes are a better choice in deep and/or very wet, heavy snow. Even walking is often a better choice.
So I think we have to be careful about the notion that one bike is going to be a lot better than the other in extremely adverse conditions. There becomes a point where nothing works well. But in more moderate snow riding conditions I think there are better bike choices than others. A bike that allows for wide tires and good power transfer is desirable in restrictive snow.
As far as ice is concerned, the tires are a much bigger issue. I prefer a wider tire because this provides a bigger contact patch with the ice and theoretically more studs hitting the ice at a given time. I can't really see where one bike is better on ice than others except for maybe one allowing for bigger tires, but my experience in ice riding is limited to a hardtail mountain bike with studded tires.