Scaled-back Pond Plan?

I was going to install a pond of approx. 6' by 10' with a section that was
around 3' deep. I'm considering scaling that back to be just a so called
"bird pond" that is around 3' by 4' feet and only 6" deep. I want the
sights and sounds of moving water but not a lot of maintenance. I'm going
to incorporate this into some new landscaping/hardscaping around the deck.

My feedback request:
- Can a keep a couple of fish in this size pond over the warm months? I
know it would be too shallow to winter them here in the northeast.
- Is this too small for a good ecosystem to "run" on its own and will
actually require more attention than a larger pond?
- Given that this would be my first pond, how likely is it that I'll want
something larger once I get a taste of having a pond?
- If I keep the surface area dimensions around 3' by 4' but go with more
depth, could I keep a couple of fish in there over the winter?

Thanks in advance.