Does it smell kinda funky? Not sweet, or "earthy" but just kind of... weird? Tree-of-Heaven (Alianthus altissima) has leaves that look like ash, and grows fast, straight, and somewhat slender, but it's got that spongey core you mentioned, and it also has an almost off-peanutbutter (some people say they smell like reeces pieces - I just think they're unique).
Tree of Heaven is also often confused for Sumac because it tends to grow in clumps like Sumac.
Tree of Heaven is the subject of the book: "A Tree Grows In Brooklyn"
If you take a picture of it, and mention whereabouts it was growing (bioregion, as well as micro-climate) I could have some more guesses for you.
PS: Have you tried making snowshoes out of it anyway?