We consulted one of our entomologists with experience identifying caterpillars, and she thinks this is a species of Underwing moth (moth subfamily Erebinae, tribe Catacalimi). In our region, there are 310 species of underwing moths and many caterpillars can look alike (especially since body coloration can be a bit variable with many species), so we can't be certain about its exact ID.

Since it sounds like it was seen recently and if it was feeding on an oak, it may be a Scarlet Underwing (Catocala coccinata). They specialize in feeding on new foliage of red oaks, and she found many caterpillars of that species last year around this time at about the same instar (stage of development). The individual in your photo is the darkest/most charcoal one she has seen, though color can vary. The horn-like projection on two of the abdominal segments are distinctive for that species, and they also will have a white underside with a pinkish cast on the under segments around 4 distinctive black dots, which it sounds like you've seen.

Miri