As arbordave says, leaves look hackberry-like, except the way the plant lays looks kinda vine-like?

Sugarberry?

Does it have thorns? Looks like a bramble. Perhaps wild raspberry.

Not it’s not a Rubus. Notice that it does not have compound leaves.

Absolutely a Celtis sp., and likely Celtis occidentalis - Common Hackberry.

Sugarberry (Sugar Hackberry) - Celtis laevigata - has a far more southerly distribution and isn't likely to be found wild in New York state.

Simple, alternate, likely rough to the touch, look for oblique leaf bases similar to Elm. Later in the season, expect to find the protuberances on the leaves indicative of the Hackberry Nipple-Gall Maker - always a great ID feature.

Not being able to see 100% of the plant, the horizontal habit in the picture doesn't indicate anything. I can find low horizontal branching like this from suckers off the shallow roots of established specimens here in the woodlands at the Valley.