I think it's ash and ash burl panels.
Casey

Not an expert here but looks like oak with burl oak panels. I'd take one of the drawers into a professional refinisher with the pics and ask what it would cost to refinish. You could go darker without hiding the grain.

Oak and ash look very similar from a distance, both being ring-porous woods. Ash tends to have a whiter tone (unless you get some dark heartwood). Red oak tends to have reds, yellows, and often some blacks in it (I was once told there were 35 different color gradings for red oak). White oak tends to be browner. But all that said, any wood can have all the color bleached out of it.

The way I tell is to look for medullary rays. Ash has none, red oak shorter ones and white oak longer ones. What medullary rays look like depends upon the orientation of the wood as cut from the log, as the rays go radially. Plainsawn will show just short lines, quarter or rift sawn will show large figure.

And just for spite, this piece is totally mitered everywhere without a square inch of end-grain to be examined for rays. A close-up and personal examination would sort it out, though. Look at the back of the dresser, the wood and finish might be labeled or chalked there. Like "mahogany, colonial" "walnut, provincial" or "oak, natural"
Casey

Thank you all so much for the information. It was good to hear someone suggest that it could be stained. I don't know anything about wood and it appears to be a nice set - I would prefer to stain it instead of replacing it. Thanks again!

You gotta' strip the old finish off before you can stain it. A lot of work for DIY, expensive to hire a refinisher. Best to just pass it on to someone who will love it for the color it is.

The frames are red oak. I dont know what the veneer panels are but they are nice and I like the color just the way it is.

I have the same set and the wood is pecan swirl.

Its a veneer of burl wood I was thold when i bought 1988

I have it too and still love it !