You can add a few drain holes with a masonry drill bit.

I had that question a few weeks ago when I had the chance to get a large, free urn. I couldn't figure out what to do and decided not to take the urn.

But then it struck me -- something I had always wanted. A small container pond that I can grow some water plants in, including having a small filter or pump for containers.

Some people even have gold fish in their container ponds, so that will take care of mosquito larvae (besides also using a larvae-killing ingredient if you don't have fish)

For your urn, maybe you can consider if you would like that before making a hole in it.

Some kind of water garden was what I was thinking myself - or at least a planter for plants that like wet feet. But back to my question of what to fill it with. It's very deep so I don't want to spend a fortune on potting soil or peat moss.

What some people do when planting regular plants in a large or deep container is to fill it with some stuff that isn't needed for the container or plants, but it's just so they don't have to fill it with so much potting soil (and to keep it lighter than being filled all up with soil).

I think the same ideas would be fine for your bog container, with the exception that you'll want to choose things which, when sitting in water all the time, won't have any adverse effects on the water or plants.

Oh, and of course, I forgot that if it becomes a water container, then just water, with a certain amount of growing medium to allow the plants to grow in.

Eg, an upside down planter, some plastic bottles, some sticks, plastic egg cartons, cut-up pieces of styrofoam, etc. Since your container is large-ish, then even 1-liter or 2-liter or 1-gallon containers might fit just fine in there.