if you didn’t own any cargo bike already, would you buy a Big Dummy or would you just put that money towards a Big Easy?

The electric cargo parks in my house get more use the non-electric ones. I could have just one, I'd go electric.

Q) Is it possible to just ride around with the battery removed or flat?

Yes, but will be heavier (even with the battery moved, because of the heavier bottom bracket. I tried this idea some, and all our e-bikes just end up getting ridden with electric. The easier thing to do is set the assist level at, say, a "1"-- the idea is just enough assist to offset the extra weight so you still get the fitness benefit of pedaling when you don' the assist.

Is it pretty much the same bike plus the weight of the motor?

The Big Easy looks looker witha more relaxed rider geometry and maybe some fatter ties by default. Overall, it's similar.

Q) I already own nice (standard) paniers, can those be clipped onto the side of these cargo bikes, or do they have a different sort of rack.

I've seen adapters before, but I can't find one quickly now. For example, see how the EdgeRunner rack has extra bar? I think panniers could hang there. These won't work on the Dummy, though. https://xtracycle.com/products/edgerunner-all-in-one-rack

Personally, I love the Carsick Design slings.

Q) Thoughts on riding an electric cargo bike in the snow/slush?

I've done that. Studded tires, fat tires and a warming planet all make this more viable. Going slower helps too.