It could bean american persimmon or even a crab apple, but I'd like to know more. The size of the red balls? Bark texture? Height of tree? Type of land? Basically anything you can add helps. Especially photos.

medlar maybe?

though I doubt it. More probably a Strawberry Tree species, Arbutus genus.

Ramona:

Can you post a photo, or a link to a photo? It'd be interesting if peanuttree is right on the medlar guess. Incidently, do you know what William Cobbett said about the Medlar in his 'American Gardener' (which was first published in London in 1821)? He said:

'MEDLAR.
A very poor thing indeed. The Medlar is propagated by grafting on crab-stocks, or pear-stocks. It is, at any rate, especially in this country, a thing not worthy of a place in a garden. At best, it is only one degree better than a rotten apple.'

Here is a link that might be useful: The Heirloom Orchardist

To me it sounds more like a Pomegranate. The fruit will often hang on through the winter and they are just putting out new leaf growth in this area. Al