I wouldn't try to wash it. You may end up with a worse mess than you have now. Dirt from the padding may work up into the cover.

Use the link to find out how to dry clean it with just soap suds. Try it on a inconspicuous place first if there is such a thing on a footstool. If the embroidery threads are old it may not be color fast. They may also be delicate.

If it were me I would just leave it alone. You might even lower the value of this antique by fooling with the cross stitch

Here is a link that might be useful: dry cleaning upholstry

leaving it alone is certainly an easier option :)) Hadn't thought of the value--thanks for bringing that up.

Rub cornstarch in to the fabric and vacuum it out....very gently! Don't rub with the vacuum just suck out the cornstarch.
A lot of the soil will come out with the cornstarch.
Are you sure it's cross stitch and not needlepoint?

Linda c

I know very little about this sort of thing, but I think you are correct. As I look at the little stitches, they are not x's. The cornstarch idea might be worth a try on the side or back first to see if it helps (the needlepoint seat part pops out of the wooden footstool). At least cornstarch is dry and might not risk getting mildewy with a liquid. thanks

Just a thought here that could be a totally bad idea, so maybe others will advise--what about foam upholstery cleaner? Seems to me it would clean the surface without too much wetting.