cleaning non-colorfast upholstery?  

Wool?
Be careful using steam if that is wool....looks like wool / wool blend to me in the close up...it could shrink or felt up badly with heat.

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Had a problem like this a while ago though not sure if it will help you, I just took the covers off, soaked them in cold water to even things out and dried them flat in the shade, originally had hung them from the wash line and even though Rothko is great it didn't look so good on my chairs.

i've used a product called...
i've used a product called "Capture" on a chair and even a couple of lampshades. comes with a pretreat that you mist on, then sift the dry powder on, brush it in, wait 30 minutes and vacuum. should probably still spot test but it's almost totally dry cleaning

Looks like wool to me,
too.
Steaming should be ok for the fabric. It's agitation that does the felting. But proceed with caution. (I don't think the creases look bad at all and they'll probably reappear anyway if you sit in the thing much.)
Steaming MAY damage the foam, though. I'd probably stick with a low temp treatment of some kind. There is a wool wash product that doesn't need to be rinsed, though you could probably rinse it if you wanted. Link below. I've never used it but it's quite popular with people who knit stuff of expensive wool yarn.
I've had good results with just the suds of a mild detergent. Put a small amount of water and some detergent (Dawn dish detergent with no dye in it is good---great at cutting oils) and shake violently. Dab the suds only onto the upholstery with a slightly-damp sponge and rub gently. Rinse by sponging with the sponge--keep wringing it out in fresh cool water. Blot with towels when dry OR vacuum out the water with a wet/dry vac.

sorry,
forgot to link to the wool wash product mentioned above.
http://www.amazon.com/Eucalan-Lavender-Fabric-Wash-Ounce/dp/B001DEJMPG/r...