Can I keep a couple of regular goldfish in there with winter temps
typically at 45-50 F during the day and about 30 F at night? Of course,
we can get temps in the teens and twenties on the odd winter day, but it
wouldn't last long. I have a pump running a bubble fountain that I plan
to remove the fountain head from to make a fatter stream of water just
gurgling up from the pond to make it less freeze prone. Do you think
the fish will survive in such a shallow pond, or should I go invest in
an aquarium and bring them in?

Invest in a $35 floating tank heater, thermostatic controlled,
instead, and your fish will do fine.