Generally speaking, the old metal machines can handle anything, as long as it fits under the foot. Walking Foot Industrials can fit 3/4" to an 1" under the foot. Just use a larger needle if you need it.
The only way to know for sure, is if you can get a small piece of the material you'll be sewing and test it.

Boy, did that picture bring up some fantastic memories! That was SO similar to the machine that I learned on! It had been my mom's, purchased around that same time frame (late '50s). I took it to college with me and she got a newer machine. It's now with my SIL, and still going strong.

I sewed vinyl on it, and faux leather, so I'd try a small piece and see how she does. You will want to get a good needle for leather, you'll break too many with your standard 10's or 12's.

Donna

Thanks for the info! I didn't have any leather to try out on it. I'm just trying to plan way ahead while I'm still studying upholstery.
It would be SO nice if I could use this machine so I can just get straight to work A.S.A.P.
That photo isn't really my machine, by the way. Just found it online.
Mine looks just like it though, except mine is cream on the door at the needle end and on the top "hood" part.
It's so pretty I sometimes leave it out with it's light on just because I like looking at it.
How weird is that?!
It's just that with the lines & curves, the paint and chrome, and the fine mechanical craftsmanship, it's like a cross between a vintage Timex and a '62 Coupe DeVille. :)

It depends on the thickness of the leather and the way the seams run. And a really good leather needle.

Thin leather - no problem
Medium leather - arrange the seams so they don't meet and you'll be OK
Heavy leather - not going to do it.